Complexes of physically interacting proteins are one of the fundamental functional units responsible for driving key biological mechanisms within the cell. Their identification is therefore necessary not only to understand complex formation but also the higher level organization of the cell. With the advent of high-throughput techniques in molecular biology, significant amount of physical interaction data has been cataloged from organisms such as yeast, which has in turn fueled computational approaches to systematically mine complexes from the network of physical interactions among proteins (PPI network). In this survey, we review, classify and evaluate some of the key computational methods developed till date for the identification of protein complexes from PPI networks. We present two insightful taxonomies that reflect how these methods have evolved over the years towards improving automated complex prediction. We also discuss some open challenges facing accurate reconstruction of complexes, the crucial ones being presence of high proportion of errors and noise in current high-throughput datasets and some key aspects overlooked by current complex detection methods. We hope this review will not only help to condense the history of computational complex detection for easy reference, but also provide valuable insights to drive further research in this area.