The bounded derived category of coherent sheaves on a smooth projective variety $X$ is a sensible and somewhat subtle invariant of $X$. Its study is tightly related to rationality problems, MMP, Mirror Symmetry, Enumerative Geometry. Semiorthogonal decompositions (SODs) are a gadget allowing one to "decompose" this category into smaller pieces. Proving the very existence of SODs is often a delicate question. In this talk we shall explain how to construct a "moduli space of SODs" attached to a smooth proper morphism of schemes; we will also discuss its main properties, and how to use it to detect indecomposability of derived categories of some smooth projective varieties. Joint work with Pieter Belmans and Shinnosuke Okawa.