In the past years, new methods are discovered for the computations of stable homotopy groups. These include Wang and Xu's RP method computing the 60 and 61 stems, which implies that the 61 dimensional sphere has unique differential structure, solving the question of uniqueness of homotopy spheres for odd dimensions. Also, Gheorghe, Isaksen, Wang and Xu developed the motivic C-tau method, which enabled the last three people to compute approximately thirty new stable homotopy groups, in dimensions 62-93. Our methodology uses motivic techniques to leverage computer calculations of both the Adams and Adams-Novikov E2-pages. I will give an account of these methods and show the phenomenons discovered in the new range.
