Since their introduction by Gromov, pseudo-holomorphic curves have been studied as maps from closed Riemann surfaces into almost complex manifolds with a taming symplectic form. This parameterized view has lead to a number of versions of Gromov compactness which are quite global in nature. For instance, in order to obtain convergence of a sequence of pseudo-holomorphic curves mapping into a family of symplectic manifolds, typically one must first assume the family has uniform bounds on geometric quantities like curvature, injectivity radius, energy threshold, etc. This talk will focus on a new approach to Gromov's compactness theorem, in which the curves are treated as generalized (unparameterized) surfaces. In particular, we prove a local compactness theorem which is useful when considering a family of target manifolds which develop unbounded geometry. This result recovers for instance compactness in the standard "stretching the neck" construction. Furthermore we will also provide applications of the local result to families of connected sums of contact manifolds in which the connecting handle degenerates to a point.