Selenium compounds play an important role in redox homeostasis in living organisms. One of their major functions is to suppress the harmful effects of hydrogen peroxide, hydroperoxides and downstream reactive oxygen species that lead to oxidative stress, which has in turn been implicated in many diseases and degenerative conditions. The glutathione peroxidase (GPx) family of selenoenzymes plays a key protective role by catalyzing the reduction of peroxides with glutathione. Considerable effort has been expended toward the discovery of small-molecule selenium compounds that mimic GPx. To date, ebselen has been the most widely studied such compound, including in several clinical trials. However, despite its proven lack of significant toxicity, it displays only moderate catalytic activity and very poor aqueous solubility. The cyclic seleninate esters and spirodioxyselenuranes have recently been investigated as potential next generation GPx mimetics, along with structurally related selenenate esters, diazaselenuranes and pincer selenuranes. Their catalytic activities, redox mechanisms and structure-activity relationships are described in this Review, along with a description and discussion of the relative merits of assays for measuring their activities.