Abstract: A formula that expresses a Laplace-type operator, i.e an operator with the metric tensor as their leading symbol, as sum of the Laplacian of a connection and an endomorphism, is called Bochner-type formula. The goal of this talk is to review the general form of Bochner type formulas and focus on some specific examples from the spin geometry, such as Lichnerowicz formula for Dirac and twisted Dirac operators.