In this talk I will present a stochastic homogenization result for free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenized random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realization and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterize the limit volume and surface integrands in terms of asymptotic cell formulas. Our homogenization result extends to the SBV-setting the classical qualitative results by Papanicolaou and Varadhan, Kozlov, and Dal Maso and Modica, which were formulated in the Sobolev setting. Some recent developments obtained in the BV setting will be also addressed. Joint work with F. Cagnetti (Sussex) , G. Dal Maso (SISSA), and L. Scardia (Heriot-Watt)