Spectra arise in almost all parts of mathematics, and often they reflect some essential information from an underlying category. Examples are: the spectrum of prime ideals of a commutative ring, the spectrum of (indecomposable) injective objects in a Grothendieck category, the Ziegler spectrum arising in the model theory of modules, and last but not least the Balmer spectrum of a tensor triangulated category. The talk will provide a survey about these spectra from a representation theory perspective, with a special focus on their interplay.