Historically, topological K-theory and its Bott periodicity have been very useful in solving key problems in algebraic and geometric topology. In this talk, we will explore the periodicities of higher real K-theories and their roles in several contexts, including Hill--Hopkins--Ravenel’s solution of the Kervaire invariant one problem. We will prove periodicity theorems for higher real K-theories at the prime 2 and show how these results feed into equivariant computations. We will then use these periodicities to measure the complexity of the RO(G)-graded homotopy groups of Lubin--Tate theories and to compute their equivariant slice spectral sequences. This is joint work with Zhipeng Duan, Mike Hill, Guchuan Li, Yutao Liu, Guozhen Wang, and Zhouli Xu.