We will discuss a conjecture stating that given a finitely generated field K equipped with a divisorial set of valuations V, an absolutely almost simple algebraic K-group G has only finitely many isomorphism classes of K-forms G′ that have good reduction at all v∈V. Originally, this conjecture came up as a tool for addressing certain questions concerning weakly commensurable Zariski-dense subgroups, which were motivated by the geometry of locally symmetric spaces (``eigenvalue rigidity’’). However, later on, other important applications (including to the genus problem and the properness of the global-to-local map in Galois cohomology) were discovered. After surveying applications, I will discuss in more detail some of the available results.