Efficient history matching of geologically complex reservoirs is important in many applications, but it is central in closed-loop reservoir modeling, in which real-time model updating is required. Within the context of closed-loop reservoir modeling, the two approaches receiving the most attention to date are ensemble Kalman filtering and gradient-based methods using Karhunen-Loeve representations (eigen-decomposition) of the permeability field. Both of these procedures are technically appropriate only for random fields (e.g., permeability) characterized by two-point geostatistics (multi-Gaussian random fields). Realistic systems are much better described by multipoint geostatistics, which is capable of representing key geological structures such as channels. History matching algorithms that are able to reproduce realistic geology provide enhanced predictive capacity and are therefore more suitable for use with field optimization. In this work, we apply a new parameterization, referred to as a kernel principal component analysis (kernel PCA or KPCA) representation, to model permeability fields characterized by multipoint geostatistics. Kernel PCA enables preserving arbitrarily high order statistics of random fields, thereby providing the capability to reproduce complex geology. The KPCA representation is then combined with an efficient gradient-based history matching technique. The linkage of KPCA for modeling geology with gradient-based history matching is very natural as the KPCA representation is differentiable and gradients with respect to geological parameters can be readily computed. The overall procedure is then applied to several example cases, including synthetic models and a model of a real reservoir. The approach is shown to better reproduce complex geology, which leads to improved history matches and better predictions, while retaining reasonable computational requirements.