During the genomic revolution, algorithmic and analytical methods for organizing, integrating, analyzing, and querying biological sequence data proved invaluable. Today, increasing availability of high-throughput data pertaining to functional states of biomolecules, as well as their interactions, enables genome-scale studies of the cell from a systems perspective. The past decade witnessed significant efforts on the development of computational infrastructure for large-scale modeling and analysis of biological systems, commonly using network models. Such efforts lead to novel insights into the complexity of living systems, through development of sophisticated abstractions, algorithms, and analytical techniques that address a broad range of problems, including the following: (1) inference and reconstruction of complex cellular networks; (2) identification of common and coherent patterns in cellular networks, with a view to understanding the organizing principles and building blocks of cellular signaling, regulation, and metabolism; and (3) characterization of cellular mechanisms that underlie the differences between living systems, in terms of evolutionary diversity, development and differentiation, and complex phenotypes, including human disease. These problems pose significant algorithmic and analytical challenges because of the inherent complexity of the systems being studied; limitations of data in terms of availability, scope, and scale; intractability of resulting computational problems; and limitations of reference models for reliable statistical inference. This article provides a broad overview of existing algorithmic and analytical approaches to these problems, highlights key biological insights provided by these approaches, and outlines emerging opportunities and challenges in computational systems biology.