Inclusive semileptonic decays of $B_{(s)}$ mesons provide an important avenue for the determination of the CKM matrix element $|V_{cb}|$ and play a central role in understanding the long-standing tension between its inclusive and exclusive determinations.
In this talk, I will discuss how inclusive semileptonic decay observables can be accessed from lattice QCD through suitably constructed four-point correlation functions and spectral reconstruction techniques. I will introduce the basic strategy and discuss the treatment of the inverse problem. I will then present recent results for inclusive semileptonic $B_s\to X_c\ell\nu$ decays, with particular emphasis on systematic uncertainties and the steps towards a controlled continuum limit.
Finally, I will discuss ongoing developments and future directions, including connections to continuum OPE calculations and the heavy-quark expansion.