This is a gentle introduction to a general theory of universal polynomials associated to classification of map-germs, called Thom polynomials. The theory was originated by René Thom in the 1950s and has since been evolved in various aspects by many authors. In a nutshell, this is about intersection theory on certain moduli spaces, say ‘classifying spaces of mono/multi-singularities of maps’, which provides consistent and deep insights into both classical and modern enumerative geometry with many potential applications.