The notion of weak Dirichlet process is the natural extension of semimartingale. Among the examples we find the following. 1. Irregular Markov processes solutions of SDEs with distributional drift with jumps. 2. Solutions of (even continuous) path-dependent SDEs with distributional drift. 3. (Path-dependent) Bessel processes. Identification problem in BSDEs driven by random measure. The talk puts the emphasis on a BSDE with distributional driver. The presentation covers joint work with E. Issoglio (Torino) and E. Bandini (Bologna).