In this study, we provide an overview of recent advances in multisensor multitarget tracking based on the random finite set (RFS) approach. The fusion that plays a fundamental role in multisensor filtering is classified into data-level multitarget measurement fusion and estimate-level multitarget density fusion, which share and fuse local measurements and posterior densities between sensors, respectively. Important properties of each fusion rule including the optimality and sub-optimality are presented. In particular, two robust multitarget density-averaging approaches, arithmetic- and geometric-average fusion, are addressed in detail for various RFSs. Relevant research topics and remaining challenges are highlighted.