This paper reviews the theory and state-of-the-art developments of the particle filter with emphasis on the remaining challenges and corresponding solutions in the context of multitarget tracking. The research focuses of the general particle filter lie on importance proposal, computing efficiency, weight degeneracy, sample impoverishment, and complicated system modelling. Multi-target tracking involves a class of complex dynamic estimation problems that require both accurate models for target birth, death and evolution, false alarms and miss-detections, and efficient decision-making strategies regarding multi-sensor data fusion and track management. Specifically, with the introduction of finite set statistics to multi-target tracking, recent years have seen the burgeoning development of a new generation of particle filters, which is referred to as the random set particle filter in this paper. Based on different scenario assumptions, different approximate forms of random set Bayesian filters can be established and implemented by the particle filter. However, manoeuvring target, unknown scenario, track management and tracker performance assessment remain key challenges for the multi-target tracking particle filter.