  This work reviews how database theory uses tractable circuit classes from
knowledge compilation. We present relevant query evaluation tasks, and notions
of tractable circuits. We then show how these tractable circuits can be used to
address database tasks. We first focus on Boolean provenance and its
applications for aggregation tasks, in particular probabilistic query
evaluation. We study these for Monadic Second Order (MSO) queries on trees, and
for safe Conjunctive Queries (CQs) and Union of Conjunctive Queries (UCQs). We
also study circuit representations of query answers, and their applications to
enumeration tasks: both in the Boolean setting (for MSO) and the multivalued
setting (for CQs and UCQs).
