Extrasolar planets
I. Speculation about their existence
Scientists have long expected stars to form with disks, and hence planets, but what happens to these planets, and their basic attributes, have been a complete mystery until recently. The idea that stars were suns, and had other earths orbiting them, was among the reasons that Giordana Bruno was burned as a heretic in 1600. But now we have detected thousands of exoplanets, and although Earthlike planets around sunlike stars are still at the edge of what we can detect, there is little doubt that will cease to be true within the decade.

II. Surprises
Although it was no great surprise that exoplanets exist, their orbital attributes are very surprising. Planets of many different sizes and many different distances from their stars have been found, such that the nice orderly sorting of our solar system into rocky planets close to the Sun, and gas giants far from it, and with a big size gap in between them, has not at all held true for exoplanets. There remain many observational selection effects based on what types we can and cannot detect, but still, it is clear that exoplanets form a highly inhomogeneous population, and so many of them are found at distances to their stars where we do not think they could have formed, implies that planetary migration, and even chaotic orbital changes, are the rule-- unlike the apparent orderly state of our own solar system.

III. Planetary migration
This is the idea that once a planet forms in a certain orbit, there are many ways that orbit can be substantially altered, especially if there are giant planets in the planetary system. First of all, giant planets require a great deal of hydrogen gas to make them giant, so they must form while there is still a disk of hydrogen gas orbiting the star. That means the gas disk can then interact with the planet, and there are several ways to do that. The two main types are called Lindblad resonances with spiral arm stuctures (such as are often seen in galaxies), and interactions with horseshoe orbits of the gas and small asteroids.

Lindblad resonances mean that an elliptical orbit is like an epicycle perturbing a circular orbit (Ptolemy did not make the up, it's one way of thinking abotu small perturbations), and so the perturbation shares the frequency of the orbit, and any driving forces in the environment that resonate with that frequency can cause gradual changes to accumulate into larger effects. Those larger effects on the disk cause spiral arms, and on the planet can cause the planet to migrate either inward or outward, depending on the details.

Horseshoe orbits are how a planet affects gas and asteroids (and other planetesmals) that have close to the same orbit as the planet. If they are a little closer to the Sun, Kepler's laws say they will catch up to the planet from behind, but that will tug them into an orbit wider than the planet, so they will lose ground an in effect be "repulsed" by the planet (as seen in the co-orbiting frame). But then later, as the planet catches up on the gas and planetesmals, the backward tug from the planet causes them to fall inward toward the Sun and speed up. That "reverses" the process and causes them to pull away from the planet, eventually coming around behind and repeating the cycle. If this happens in a symmetric way, there is no net effect on the planet, but other processes, like feeding in new dust and gas from other regions of the solar system, can cause asymmetric behavior, and that can also induce planetary migration either inward or outward.

These types of planetary migrations that involve interaction with the gaseous disk and/or a very full disklike population of planetesmals allow planets to ultimately orbit at distances where they could not have formed, and contribute to the "hot Jupiter" phenomenon in exoplanet detection.

Another form of planetary migration, which happens between the planets themselves or the large planetesmals, is gravitational scattering. This is like how the Voyager satellite was able to make a Grand Tour of all the outer planets using gravitational assists from each one, and ultimately leave the solar system. This was a delicately planned orbit, but an orbit nevertheless, in the sense that it could have conceivably happened naturally-- given enough time. So in the huge number of systems, and the huge amount of available time, almost any dynamics we can imagine could have happened somewhere. Coupled with the anthropic principle that says our own system might be quite special because it led to us, makes it very difficult to understand or predict exactly what happened in our own case! Ergo ideas like the "Grand Tack" of Jupiter.