In this talk I will explain how to define a notion of Hermitian K-theory for stable $\infty$-categories and how this is related with classical notions of Grothendieck-Witt theory and L-theory. We will use the properties of these invariants to compute the hermitian K-theory groups for Dedekind domains in term of other invariants like the K-groups and the Picard group. This is joint work with B. Calmès, E. Dotto, Y. Harpaz, F. Hebestreit, M. Land, K. Moi, T. Nikolaus and W. Steimle.