Being one of the main proteins in the human body and many animal species, albumin plays a decisive role in the transport of various ions—electrically neutral and charged molecules—and in maintaining the colloidal osmotic pressure of the blood. Albumin is able to bind to almost all known drugs, as well as many nutraceuticals and toxic substances, largely determining their pharmaco- and toxicokinetics. Albumin of humans and respective representatives in cattle and rodents have their own structural features that determine species differences in functional properties. However, albumin is not only passive, but also an active participant of pharmacokinetic and toxicokinetic processes, possessing a number of enzymatic activities. Numerous experiments have shown esterase or pseudoesterase activity of albumin towards a number of endogeneous and exogeneous esters. Due to the free thiol group of Cys34, albumin can serve as a trap for reactive oxygen and nitrogen species, thus participating in redox processes. Glycated albumin makes a significant contribution to the pathogenesis of diabetes and other diseases. The interaction of albumin with blood cells, blood vessels and tissue cells outside the vascular bed is of great importance. Interactions with endothelial glycocalyx and vascular endothelial cells largely determine the integrative role of albumin. This review considers the esterase, antioxidant, transporting and signaling properties of albumin, as well as its structural and functional modifications and their significance in the pathogenesis of certain diseases.