In this talk, I will describe an efficient way of compactifying moduli spaces of J-holomorphic maps relative to simple normal crossings (snc) symplectic divisors, including the holomorphic case.  The primary goal of this construction is to define Gromov-Witten invariants relative to snc divisors, and to establish a GW-degeneration formula for any semistable degeneration with an snc central fiber. It is also possible to extend the construction to the case of J-holomorphic maps with boundary on a Lagrangian, even if the Lagrangian intersects the divisor non-trivially (intersecting each stratum in a Lagrangian again); especially, if the Lagrangian is a real locus.