Peroxiredoxins (Prdxs) are thiol proteins that function both as antioxidants and as regulators of cell signaling. This article focuses on the biological chemistry of mammalian typical 2-Cys Prdxs and how their molecular properties relate to cellular function. These Prdxs operate through a complex mechanism that involves redox changes at two active sites, coupled to conformational changes and reversible oligomerization. The reduced forms react extremely rapidly with H2O2 but, paradoxically for efficient antioxidants, condensation of the resultant sulfenic acid to the intramolecular disulfide is remarkably slow. Consequently, turnover plateaus as the H2O2 concentration rises and further slows as oxidized thioredoxin accumulates and recycling becomes limited. Therefore, these Prdxs are potent scavengers of H2O2 at low concentrations but are less well equipped for high fluxes. The biochemical properties of Prdxs are well suited for sensing H2O2 and relaying oxidation to less reactive thiol proteins in redox-regulated signaling pathways. Several relays have been well characterized, but it is proving challenging to establish whether this is a widespread signaling mechanism in mammalian cells. An alternative signaling mechanism is for Prdxs to act as negative regulators. This requires the direct oxidation of signaling proteins that bypasses the efficient reaction of H2O2 with Prdxs. Various mechanisms have been proposed, but most remain speculative. Overall, although we have detailed knowledge of the properties of mammalian Prdxs and evidence that they perform important cell functions, there are still major mechanistic gaps to bridge between the two.