Given a non-contractible homotopy type X, we have three notions of how X is "bounded": 1. X being homotopy equivalent to a finite dimensional CW complex; 2. the homology of X vanishes above a certain degree; 3. the homotopy groups of X vanish above a certain degree. If X is simply connected, it turns out that notion 1 and 2 agree, while notion 2 and 3 are mutually exclusive. In this talk, we are going to present a theorem by McGibbon-Neisendorfer describing this phenomenon, which has a very short proof using the solved Sullivan conjecture. If time permits, we will also discuss some stable analogs.