Protein-Protein Interaction (PPI) networks are believed to be important sources of information related to biological processes and complex metabolic functions of the cell. When studying the workings of a biological cell, it is useful to be able to detect known and predict still undiscovered protein complexes within the cell's PPI networks. Such predictions may be used as an inexpensive tool to direct biological experiments. The increasing amount of available PPI data necessitate a fast, accurate approach to biological complex identification. Because of its importance in the studies of protein interaction network, there are different models and algorithms in identifying functional modules in PPI networks. In this paper, we review some representative algorithms, focusing on the algorithms underlying the approaches and how the algorithms relate to each other. In particular, a comparison is given based on the property of the algorithms. Since the PPI network is noisy and still incomplete, some methods which consider other additional properties for preprocessing and purifying of PPI data are presented. We also give a discussion about the functional annotation and validation of protein complexes. Finally, new progress and future research directions are discussed from the computational viewpoint.