This short paper reviews the main contributions of our recent work on static analysis of existential rules (a.k.a. tuple-generating dependencies). Between such rules, several kinds of logical relationships – also called dependencies in an unfortunate clash of terminology – are of interest, but their computation highly intractable ( Σ P2 -complete). We develop new, optimised procedures for this task, and present a prototype implementation that scales to rule sets with more than 100,000 rules. This allows us to perform much faster acyclicity checks and to identify rule sets that admit e ffi cient core computation via the standard chase.