The main result of this paper is a compactness theorem for families of functions in the space SBV (Special functions of Bounded Variation) defined on periodically perforated domains. Given an open and bounded set \({\Omega\subseteq\mathbb{R}^n}\), and an open, connected, and (−1/2, 1/2)n-periodic set \({P\subseteq\mathbb{R}^n}\), consider for any e > 0 the perforated domain Ωe := Ω ∩ eP. Let \({(u_\varepsilon)\subset SBV^p(\Omega_{\varepsilon})}\), p > 1, be such that \({\int_{\Omega_{\varepsilon}}\left|{\nabla{u}_\varepsilon}\right|^pdx+\mathcal{H}^{n-1}(S_{u_\varepsilon}\,\cap\,\Omega_{\varepsilon}) +\left\Vert{u_\varepsilon}\right\Vert_{L^p(\Omega_{\varepsilon})}}\) is bounded. Then, we prove that, up to a subsequence, there exists \({u\in GSBV^p\,\cap\, L^p(\Omega)}\) satisfying \({\lim_\varepsilon\left\Vert{u-u_\varepsilon}\right\Vert_{L^1(\Omega_{\varepsilon})}=0}\). Our analysis avoids the use of any extension procedure in SBV, weakens the hypotheses on P to the minimal ones and simplifies the proof of the results recently obtained in Focardi et al. (Math Models Methods Appl Sci 19:2065–2100, 2009) and Cagnetti and Scardia (J Math Pures Appl (9), to appear). Among the arguments we introduce, we provide a localized version of the Poincare-Wirtinger inequality in SBV. As a possible application we study the asymptotic behavior of a brittle porous material represented by the perforated domain Ωe. Finally, we slightly extend the well-known homogenization theorem for Sobolev energies on perforated domains.