In this review article, we provide general information on the known methods for directed synthesis of 3- and 4-aminofuroxans, as well as analyze the main aspects of their reactivity. Methods for regio- and chemoselective transformations of aminofuroxans are considered in detail, including both classical reactions involving oxidation, acylation, and nitration, as well as several intramolecular rearrangements of aminofuroxans, resulting in the formation of various nitrogen-containing heterocyclic systems. Particular attention has been focused on mechanistic details of these reactions, as well as the practical significance of the synthesized compounds for pharmacology and materials science.