We present a tool and theory RE# for regular expression matching that is built on derivatives, does not use backtracking, and, in addition to the classical operators, also supports complement, intersection and restricted lookarounds. We develop the theory formally and show that the main matching algorithm has input-linear complexity both in theory as well as experimentally. We apply thorough evaluation on popular benchmarks that show that RE# is over 71% faster than the next fastest regex engine in Rust on the baseline, and outperforms all state-of-the-art engines on extensions of the benchmarks often by several orders of magnitude.