Protein tyrosine phosphatases (PTPs) play a critical role in physiological signaling pathways by controlling the level of tyrosine phosphorylation. The past decade has seen a vast increase in both academic and industrial interest in PTPs and their relevance as potential therapeutic targets, with several PTP inhibitors recently entering clinical trials. Despite these developments, there are numerous examples of failed PTP drug discovery programs, such that PTPs have attained a reputation as `undruggable' targets. This review attempts to illustrate the many obstacles that must be overcome to successfully develop a PTP drug, ranging from validation of PTPs as therapeutic targets to the difficulties of assessing the true inhibitory nature of apparently well-behaved compounds, along with the need to balance the physiocochemical properties required for active site binding with the characteristics needed for in vivo activity. A number of examples of structure-based design are presented, along with cautionary tales of PTP inhibitor programs that have failed due to unexpected shortcomings.