The CKM matrix element $|V_{cb}|$ has been measured from the semi-leptonic inclusive and exclusive $B$ meson decays with the Standard Model hypothesis. This proceedings review recent studies on New Physics effects related to these $|V_{cb}|$ measurements. In short, one can find that NP with $\sim 5\%$ of the SM size could be allowed consistently with Belle data for the $\bar B \to D^{(*)} \ell \nu$ processes and theory evaluations for the form factors. A corresponding LHC study is also presented, in which $\ell^\pm + \text{missing}$ searches with data available by ATLAS can probe New Physics signal.