Can't seem to do it.
The animations play fine elsewhere.
Ideas???

There are several possibilities for this, I suggest you to add a little more details about the problem. Make sure when you export FBX, you have to specify the range of frames to export. In Unity, remember to create an Animator and add it to your character.
Or, if you add key frames to geometries directly other than bones, Unity doesn't support vertex animation in FBX, so the animation won't play in Unity. But I found that we can make vertex animation by exporting digital asset to Unity, and it can bake vertex animation for us. Oddly enough, digital asset can't bake the animation created by bones.