Astrogation is quite an art despite the obvious scientific aspects. In a significant way, it is more of an art than navigation on land or sea. The total predictability of ballistic trajectories allows one to work what appear to be wonders not only to those who do not know what mathematics went into the feat, but especially those who do.
Marion and Thornton, in their classical mechanics textbook, give an example of astrogation as a performance art. Scientists found that there was going to be a near-Earth comet, and wanted to intercept it with something so as to be able to study it. They had a lot of warning time. So they took a satellite that was on a less important project, and pushed it a very little bit to one side a long time in advance. Across a period of several months, the satellite coasted off, curled around the moon a few times, wandered by the Earth-Moon lagrange points, and went in very strange and apparently irrelevant directions. But when the comet arrived, satellite had been aimed with such precision that it passed THROUGH the tail of the comet. I am sorry that E2 can't make a no-pictures exception here, since the diagram of the comet's orbit gives a much better idea of the dance that satellite went through to get to that comet.
However, things do not need to be that complicated if you have more to work with than maneuvering jets. The most efficient way to boost into a higher circular orbit than the one you're already in (assuming you are...) is to briefly thrust in the direction you're moving, then wait half an orbit and fire again.
But things usually are complicated enough that the proverbial rocket scientist is earning eir reputation. The main problem is that if you're not just trying to get into an orbit somewhere, you must rendezvous. And you can't get to the location only - you hav to match velocity. Timing is critical, even if it's on the scale of weeks. Opportunities come and go, as we pass the slower-moving outer planets, and are in turn passed by Mercury and Venus. The extraordinary opportunity for long-term predictability due to the high vacuum lets 18th century physics rule 20th and 21st century endeavors.