Abstract: The notion of a radical of a ring was first suggested by Wedderburn in 1908 and first used by Koethe in 1930. We say a class of rings C is a radical class of rings if it is homomorphically closed, the sum of all ideals in C of a ring R, denoted by C(R), is again in C, and C(R/C(R))=(0). We call C(R) the radical of R associated to the class C. The idea of radical theory is to collect ring theoretical information in C(R) and be able to then give more information about R. In this talk we will discuss some of the classical results in radical theory and describe some of modern techniques being used in current research. In particular, techniques from graded-ring theory and theoretical computer science will be discussed. This talk will be accessible to a general mathematical audience