A colored network model, corresponding to a colored graph in mathematics, is used for describing the complexity of some inter-connected physical systems. A colored network is consisted of colored nodes and edges. Colored nodes may have identical or nonidentical local dynamics. Colored edges between any pair of nodes denote not only the outer coupling topology but also the inner interactions. In this paper, first, synchronization of edge-colored networks is studied from adaptive control and pinning control approaches. Then, synchronization of general colored networks is considered. To achieve synchronization of a colored network to an arbitrarily given orbit, open-loop control, pinning control and adaptive coupling strength methods are proposed and tested, with some synchronization criteria derived. Finally, numerical examples are given to illustrate theoretical results.