Why is it I can move an animated model after importing but not later? When I import a model, say an .fbx, I'm able to move the model and its accompanying animation anywhere in the scene I want. However, once I select something else, the model and its animation become set in place and there's apparently no effective way to re-select it (and everything about it) and move it somewhere else. I'm talking about a complex character model, not just a cube.

A related issue is that I have an imported, animated model (a dancer) and I want to duplicate it and move the duplicate. Same issue though, I can't drag the newly duplicated version without the model distorting like crazy. 

Am I missing something?
A complex animated character consists of two parts, a mesh object and a rig that deforms it. When you move one of these paired objects in object mode the armature deformation goes bad, you need to move both objects together. Usually the armature is made the parent of the object, so moving the armature keeps it all together but moving the mesh object will be an issue.

In 2.7x while an armature is in pose mode, we can select an object and the armature will be deselected. In 2.80 this changes, while in pose mode we are unable to select another object. The solution is to go into object mode to select another object. This is also true for other modes, we need to be in object mode to select a different object.