 The introduction of structuralist views in the philosophy of mathematics is often assumed to have happened in the 1960s, in works by Paul Benacerraf and Hilary Putnam; the trend picked up steam in the 1980s–90s, when Michael Resnik, Stuart Shapiro, Geoffrey Hellman, Charles Parsons, and others entered the fray; and these debates have been reshaped again during the last 20 years, by several philosophical challenges to structuralism and by the introduction of further variants, including category-theoretic forms of structuralism. Besides introducing the reader to the general topic of “structuralism in the philosophy of mathematics”, a second main goal of the present essay will be to provide a novel, broader, and relatively comprehensive taxonomy for the varieties of structuralism on offer today. 