Many essential cellular processes such as signal transduction, transport, cellular motion and most regulatory mechanisms are mediated by protein-protein interactions. In recent years, new experimental techniques have been developed to discover the protein-protein interaction networks of several organisms. However, the accuracy and coverage of these techniques have proven to be limited, and computational approaches remain essential both to assist in the design and validation of experimental studies and for the prediction of interaction partners and detailed structures of protein complexes. Here, we provide a critical overview of existing structure-independent and structure-based computational methods. Although these techniques have significantly advanced in the past few years, we find that most of them are still in their infancy. We also provide an overview of experimental techniques for the detection of protein-protein interactions. Although the developments are promising, false positive and false negative results are common, and reliable detection is possible only by taking a consensus of different experimental approaches. The shortcomings of experimental techniques affect both the further development and the fair evaluation of computational prediction methods. For an adequate comparative evaluation of prediction and high-throughput experimental methods, an appropriately large benchmark set of biophysically characterized protein complexes would be needed, but is sorely lacking.