invariant theory is a beautiful field. the area dates back over 100 years to the work of hilbert, klein, gauss, and many others. it is a very active area of research today, particularly from the viewpoint of algebraic geometry and combinatorics. it also has far reaching applications in representation theory, coding theory, mathematical modeling, and even air target recognition. (i just happened to run across this last application on google and it will *not* be explained.) in this talk, i aim to illustrate the beauty of noncommutative invariant theory. all basic notions will defined. namely, i will explain the noncommutative analogues of each of the following terms: "groups", "acting on", "polynomial rings". i will also provide an overview of recentwork pertaining to quantum group actions on (noncommutative) regular algebras. the results discussed here are from joint works with kenneth chan, pavel etingof, ellen kirkman, yanhua wang, and james zhang: see arxiv:math/1210.6432, 1211.6513, 1301.4161, 1303.7203.