Complexes of physically interacting proteins constitute fundamental functional units that drive almost all biological processes within cells. A faithful reconstruction of the entire set of protein complexes (the complexosome) is therefore important not only to understand the composition of complexes but also the higher level functional organization within cells. Advances over the last several years, particularly through the use of high-throughput proteomics techniques, have made it possible to map substantial fractions of protein interactions (the interactomes) from model organisms including Arabidopsis thaliana (a flowering plant), Caenorhabditis elegans (a nematode), Drosophila melanogaster (fruit fly), and Saccharomyces cerevisiae (budding yeast). These interaction datasets have... enabled systematic inquiry into the identification and study of protein complexes from organisms. Computational methods have played a significant role in this context, by contributing accurate, efficient, and exhaustive ways to analyze the enormous amounts of data. These methods have helped to compensate for some of the limitations in experimental datasets including the presence of biological and technical noise and the relative paucity of credible interactions.(#br)In this book, we systematically walk through computational methods devised to date (approximately between 2000 and 2016) for identifying protein complexes from the network of protein interactions (the protein-protein interaction (PPI) network). We present a detailed taxonomy of these methods, and comprehensively evaluate them for protein complex identification across a variety of scenarios including the absence of many true interactions and the presence of false-positive interactions (noise) in PPI networks. Based on this evaluation, we highlight challenges faced by the methods, for instance in identifying sparse, sub-, or small complexes and in discerning overlapping complexes, and reveal how a combination of strategies is necessary to accurately reconstruct the entire complexosome.(#br)The experience gained from studying model organisms has immensely helped in mapping of interactions and identifying protein complexes from higher-order organisms including Homo sapiens (human) and other mammals. In particular, with the increasing use of panomics techniques spanning genomics, transcriptomics, and proteomics to map human cells across multiple layers of functional organization, the need to understand the basis of rewiring of the interactome (e.g., as a result of changes to the genome), and the resulting recomposition of protein complexes, is gaining immense importance. Toward this end, recent computational methods have integrated panomics datasets to assess interactome rewiring and to track complexes across conditions (e.g., between normal development and disease). These efforts have revealed valuable insights into dysregulated cellular processes, and highlighted molecular targets for therapeutic intervention in diseases including cancer. By discussing these approaches in depth, we emphasize how tackling a fundamental problem such as protein complex prediction (PCP) can have far-reaching applications in understanding the biology underpinning physiological and environmental transformations affecting cells.