Zero-suppressed binary decision diagrams (ZDDs) are a data structure representing Boolean functions, and one of the most successful variants of binary decision diagrams (BDDs). On the other hand, BDDs are also called branching programs in computational complexity theory, and have been studied as a computation model. In this paper, we consider ZDDs from the viewpoint of computational complexity theory. Our main proposal of this paper is that we regard the basic idea of ZDDs as a new computation, which we call zero-suppressed computation. We consider the zero-suppressed version of two classical computation models, decision trees and branching programs, and show some results. Although this paper is mainly written from the viewpoint of computational complexity theory, the concept of zero-suppressed computation can be widely applied to various areas.