Since the Earth has a shorter orbital period than Mars, we pass in between Mars and the Sun on a fairly regular basis (on the average, every 780 days, or 2 years and 50 days). When we do, we see Mars in the opposite direction from the Sun, at opposition (see Planetary Aspects for more about general positions of the planets relative to each other). At that time we are also about as close as we can be during that particular two-year interval, or synodic period of revolution.
 If Mars' orbit were nearly circular, as ours is, each time we lap Mars the two planets would be about the same distance from the Sun as usual, and our distance from Mars would be about the same -- a little less than 49 million miles, which is the difference between our orbital sizes. But Mars' orbit is not as circular as ours, having an eccentricity of 0.093, which means that its distance from the Sun varies by a little over 18%, or nearly 28 million miles. As a result, depending upon where Mars is in its orbit when we lap it, we can pass as little as 35 million miles from it (if it is near perihelion), or as much as 63 million miles from it (if it is near aphelion).
 As shown in the diagram below, the approximately 2 years and 2 months synodic period of Mars means that wherever we lap Mars in one synodic period, we will lap it a little further along in its (and our) orbit the next time. So if it is near perihelion at one opposition and relatively close to us as it was in 2003, at subsequent oppositions it will be further and further from perihelion, and further and further from us until it is near aphelion at opposition, and as far from us as possible for an opposition, as it was in 2010 and 2012; then it will be closer and closer to perihelion and to us at each succeeding opposition until the next perihelion opposition, which occurs every seven or eight synodic periods, or 15 to 17 years after the previous perihelion opposition.

 Above, a diagram showing the relative position of the Earth and Mars at various oppositions from 1995 to 2020 (with lines between the planets in black for oppositions from 1995 to 2007 and in red for later ones). The distance (in Mmi, or millions of miles) between the Earth and Mars at closest approach is also shown. In general, the closer Mars is to perihelion at opposition the closer it is to the Earth, and the closer it is to aphelion at opposition the further it is from the Earth. But although opposition and closest approach are close together at perihelion (as in 2003) and aphelion (as in 2012), if Mars is moving away from the Sun (meaning it is between perihelion and aphelion), closest approach is several days earlier than opposition. Similarly, if Mars is moving toward the Sun (meaning it is between aphelion and perihelion), closest approach is several days later than opposition. As a result the distance at closest approach can be somewhat different than might be expected based only on Mars' position at opposition.
 Note that (1) the date of opposition corresponds to the Earth's position in its orbit (we are at the point marked by the direction to the Vernal Equinox on the first day of autumn, in late September), so the dates are steadily later in the year as you move eastward (counterclockwise) around the orbits; (2) each opposition is further along the orbits of the Earth and Mars, because it takes just over two years for the Earth to lap Mars; and (3) when Mars is near perihelion and moving faster, it takes longer for the Earth to "catch up" with it and successive oppositions are further apart than usual, whereas when Mars is near aphelion and moving slower it takes less time for the Earth to catch up with Mars, and successive oppositions aren't as far apart as usual.

 The diagram above, although a good representation of our relative position and distance from Mars at various oppositions, only shows less than two full series of oppositions (all the way around the orbit). The table below lists all oppositions from 1995 to 2037, covering just over two series of oppositions, and shows that we were relatively close to Mars in 2001 and 2005, exceptionally close in 2003, and will be relatively close to Mars in 2020 and 2033, and within a million miles or so of the 2003 distance in 2018 and 2035.
 Note the following characteristics of the table (and the confirmation it gives of the statements made in the discussion of the diagram, above):
(1) Two dates are shown -- the date of opposition, when the Earth passes between Mars and the Sun, and the date of closest approach, which is a few days earlier than opposition when Mars is moving away from the Sun (and the Earth), and a few days later than opposition when Mars is moving toward the Sun (and the Earth).
(2) If the date of opposition is very close to perihelion, so that the date of closest approach is almost the same as the opposition date as it was in 2003, we pass closer to Mars than if the date is further from perihelion, as it will be in 2018 and 2035.
(3) When we are lapping Mars near its perihelion, it takes longer to lap it than usual (almost 2 years and 2 months), because it is moving faster in that part of its orbit; and when we are lapping Mars near its aphelion, it takes less time to lap it than usual (just over 2 years and 1 month), because it is moving slower in that part of its orbit.

The Closest Opposition in 59,619 Years
 You have probably heard at some time in the last few years that Mars was closer to the Earth than at any time in the last 60,000 years. This was essentially true during the 2003 opposition, which was the closest approach of the two planets since 57,617 BC, when Mars was about twenty-five thousand miles closer (about 34,621,500 miles from Earth, versus 34,646,418 miles in 2003). You may not have heard, however, that we will be even closer to Mars at various times in the next millenium, and closer yet during each of the next twenty millenia. Why is this?
 If the orbits of the Earth and Mars were absolutely fixed we would sometimes be a little closer to Mars at the nearest opposition in any 15 to 17 year period and sometimes further away, but the very closest approaches would be more or less the same distance, as shown in the table above. However, our orbit and that of every other planet, including Mars, is subject to small changes or perturbations caused by the gravitational effect of the planets on each other. If only the Sun influenced our motion, our orbit would be nearly fixed in space; but every time that Mercury or Venus laps us, or we lap one of the outer planets, the gravitational attraction of each planet for the other very slightly changes the orbit of each planet.
 The effects of these individual perturbations is very small, because the planets are much smaller than the Sun and exert much less force on each other than the Sun does on any of them. In addition, perturbations which occur in one part of an orbit change the orbit in one way, while perturbations which occur in another part of the orbit change the orbit in the opposite way. This will be discussed in more detail later, on a page about how Neptune controls the orbit of Pluto and the "Plutinos", but to summarize the effects, if Mars is moving away from the Sun when we lap it we slow it down a little, which tends to make its orbit smaller and its orbital period shorter; while if Mars is moving toward the Sun when we lap it we speed it up a little, which tends to make its orbit bigger and its orbital period longer. And since, as shown in the diagram above, we lap it at different places at different times, the perturbations mostly cancel each other out over long periods of time.
 This does not mean, however, that they exactly cancel out, and as a result every planet's orbit tends to "wobble" slightly relative to its average orbit; or more accurately, the numbers which describe the orbits tend to slowly swing back and forth relative to their average values.
 As shown in the diagram below, this effect applies (among other things) to the eccentricity of Mars' orbit. Over very long periods of time the eccentricity averages about 5 or 6%, but there are times such as now when the eccentricity is larger; times such as 200,000 years from now, when the eccentricity is almost twice the average value, or nearly 12%; and times such as a million years ago and in the future when the eccentricity is close to 0.

 Over long periods of time the eccentricity of Mars' orbit varies as a result of perturbations by other planets (primarily Jupiter), from as little as 0% to as much as 12%. (Jean Meeus; retrieved from Internet Archive Wayback Machine)

 At those times when its orbital eccentricity is small, Mars' distance from the Sun hardly changes and as a result its opposition distance from us is relatively constant; but at those times when its eccentricity is large, Mars is substantially closer to the Sun at perihelion and substantially further away at aphelion, and therefore unusually close to us at perihelion oppositions and unusually far from us at aphelion oppositions.
 As it happens, Mars had a substantially higher orbital eccentricity about 90,000 years ago, and for most of the next 60,000 years its eccentricity was gradually decreasing; while for the last 30,000 years and the next 20,000 years its eccentricity has been and will be gradually increasing. This means that over long periods of time, the distance between the Earth and Mars at perihelion oppositions is gradually getting smaller and smaller, and 20,000 years from now that distance will be a few million miles smaller than it can ever be in the current era. It also means that for the last 30,000 years, while the eccentricity of Mars' orbit gradually increased, the perihelion opposition distance has been gradually getting smaller. This doesn't mean that every perihelion opposition is going to involve smaller distances; as shown in the table above, the next few perihelion oppositions will be a little further than the most recent one, simply because they aren't quite as close to the exact date of perihelion. Still, the closest oppositions are gradually getting very slightly closer. In recent years there were close approaches on Aug. 18, 1845 and Aug. 23, 1924, which were only thirty thousand miles further than the 2003 opposition; and in coming years there will be still closer oppositions, starting with the approach of August 28, 2287; but since that's a long ways away, the 2003 opposition is at least slightly remarkable, no matter how you look at it.

To be added in the next iteration of this page: A diagram showing the oppositions of the Earth and Mars from 2020 to the mid 2040's or 50's, and an extension of the table of oppositions and closest approaches to comparable dates. Also, a link to a new page about Hohmann Transfer Orbits (or Least-Energy Orbits), showing how much easier it is to reach Mars at perihelion than at aphelion (though that depends only on the dates of perihelia, not on oppositions, which determine how close the Earth is to Mars when lapping it, but do not affect the dates required for launches reaching Mars at perihelion).