The activity in the living cell is carried out by a myriad network of interactions between macromolecules. These include interactions between proteins that form a functional complex, a protein modifying another protein in a transient interaction, a transcription factor that binds a specific DNA locus triggering a change in chromatin or transcription, and so on. Characterization of these interactions in terms of timing, context, and function is crucial for understanding how cells carry out basic biological processes. The recent years have led to the introduction of many assays for probing these interactions in a systematic and large-scale manner. However, there is a large gap between assay results and understanding of biological systems. The challenge for computational methods is to bridge this gap by combining results of different assays and introducing statistical methodologies. In this review we discuss recent advances in approaches dealing with these challenges, and key directions for the future.