Human serum albumin (HSA) is an abundant and highly soluble plasma protein with the capacity to bind a remarkably diverse set of lipophilic anionic compounds so that it fulfils important roles in the transport of nutrients, hormones and toxins. The protein attracts great interest from the pharmaceutical industry since it can also bind a variety of drug molecules, impacting their delivery and efficacy. Our understanding of the binding and transport properties of albumin has been transformed by structural studies of the protein, in which crystallographic analysis has played a leading role. This review summarises the main insights to have accrued from this work, highlighting the significant advances that have been made but also pointing out some of the challenges ahead. Since further progress is likely to benefit from increased structural scrutiny of HSA, methodological developments instrumental to the success of crystallographic analysis of the protein are discussed in some detail.