We present the data model, design choices, and performance of ProvSQL, a general and easy-to-deploy provenance tracking and probabilistic database system implemented as a PostgreSQL extension. ProvSQL's data and query models closely reflect that of a large core of SQL, including multiset semantics, the full relational algebra, and aggregation. A key part of its implementation relies on generic provenance circuits stored in memory-mapped files. We propose benchmarks to measure the overhead of provenance and probabilistic evaluation and demonstrate its scalability and competitiveness with respect to other state-of-the-art systems.