  Feder and Vardi’s conjecture led to an extremely productive research program.   In particular, a rich algebraic theory of CSPs was developed in a number of papers starting with [Jeavons et al. 1997]; see [Bulatov, 2018] for a survey. Eventually, by applying and advancing this algebraic theory, Bulatov and Zhuk independently proved the Feder and Vardi conjecture [Bulatov, 2017; Zhuk, 2017].  