Is there any way to animate specific vertices instead of the whole object? I'm starting to do my first form of (somewhat) major animation in blender, before I've only done things like keyframes on text extrude, object size movement, etc. I want to warp an object in a specific sort, but I've tried creating keyframes on vector positions, and it doesn't seem to work! Is there any way to animate specific vertices instead of the whole object? Thanks!
To do this you need to create shapekeys and then keyframe their influence/strength. 

Shapekeys are essentially alternative shapes for you mesh that allow you to interpolate between them and the base shape of the mesh. 

see the blender manual for more details