After Effects is very powerful when it comes to make animations that automatically react to the music or the sounds of your project. Here I give an overview over the most common workflows.
BeatEdit is an extension for After Effects (and also Premiere Pro) which can auto-detect beats in a music track, wiggle to the beat, write markers, repeat keyframes, stagger layers, and more!
Audio keyframes and expressions
The keyframe assistant "Convert Audio to Keyframes" (AE menu: Animation→Keyframe Assistant→Convert Audio to Keyframes) creates a layer with some slider that represent the audio volume of your music. At each point in time, the value of this slider tells you, how loud the music is at that point in time. Now you can use normal expressions or Linking iExpressions to connect any properties to it. Compared to Beat Assistant, animations created with this technique look more fuzzy, since the audio volume is not as regular as the beats detected by Beat Assistant
With Audio iExpressions you can refine the technique explained in the previous section. Various Beat Detector iExpressions allow to react to other aspects of the music than just the pure volume using various Beat Detectors. To these beat you then connect any property using one of the Change on Beat iExpressions. If you want to move the position of a 2D layer, for example, you use the Change on Beat 2D iExpression and if you want to modify some text at each beat you use the Change on Beat Text instead.