Tensor-triangular geometry was initiated in the early 2000s by Paul Balmer to give a unified geometric framework for studying tensor-triangulated categories, arising in disparate areas such as modular representation theory and algebraic geometry. Given a monoidal triangulated category, this theory produces a topological space, the Balmer spectrum, which in many cases parametrizes the thick ideals of the category, and is defined in an analogous way to the spectrum of a ring. We consider derived categories of schemes and stable categories of finite tensor categories as examples; in the latter case, we conjecture that the Balmer spectrum corresponds to the projective spectrum of the cohomology ring. We also give examples of computing the Balmer spectrum of categories skewed by group actions. This talk will include joint with with Nakano—Yakimov and Hongdi Huang.