In this paper, I motivate the use of abstraction in game-playing, describe various kinds of abstraction that might be useful in game-playing and planning, and show how they can all be subsumed under a unifying definition of abstractions. I propose a methodology for abstraction research that involves translating existing CGP methods into a language of abstraction networks before trying to generalize those methods to work with a variety of types of abstractions. I then summarize the results of my master's thesis work, in progress, on applying decision-theoretic techniques to do effective and efficient reasoning within the abstraction-network framework.