The recently measured first few moments of the $q^2$ distribution in inclusive semi-leptonic $B$ decays are of great interest for the extraction of $|V_{cb}|$ from inclusive decays.
In this talk we review the theoretical calculation of the $q^2$ moments and their inclusion into the global fit for the extraction of HQE parameters and $|V_{cb}|$.
We discuss the improvements and features of the fit, paying attention to the treatment of correlations.
Our updated value is $|V_{cb}| = (41.97 \pm 0.48) \times 10^{−3}$.