Why not have a computer just draw a map? This is something you hear a lot when people talk about gerrymandering, and it's easy to think at first that this could solve redistricting altogether. But there are more than a couple problems with this idea. In this chapter, two computer scientists survey what's been done in algorithmic redistricting, discuss what doesn't work and highlight approaches that show promise. This preprint was prepared as a chapter in the forthcoming edited volume Political Geometry, an interdisciplinary collection of essays on redistricting. (https://mggg.org/gerrybook)