Protein–protein interactions (PPIs) control the assembly of multi-protein complexes and, thus, these contacts have enormous potential as drug targets. However, the field has produced a mix of both exciting success stories and frustrating challenges. Here, we review known examples and explore how the physical features of a PPI, such as its affinity, hotspots, off-rates, buried surface area and topology, might influence the chances of success in finding inhibitors. This analysis suggests that concise, tight binding PPIs are most amenable to inhibition. However, it is also clear that emerging technical methods are expanding the repertoire of ‘druggable’ protein contacts and increasing the odds against difficult targets. In particular, natural product-like compound libraries, high throughput screens specifically designed for PPIs and approaches that favour discovery of allosteric inhibitors appear to be attractive routes. The first group of PPI inhibitors has entered clinical trials, further motivating the need to understand the challenges and opportunities in pursuing these types of targets.