Multi-Robot Multi-Target Tracking (MR-MTT) addresses the problem that a swarm of mobile robots actively detect and move to maintain surveillance of a team of dynamic targets, which is a fundamental problem in the modern robot system and has enormous potential in numerous fields. This paper investigates a series of MR-MTT algorithms, with detailed demonstrations of two distributed approaches to solving MR-MTT in finite iterations. On the one hand, a novel local algorithm is introduced to solve multi-robot multi-target assignments within limited communication rounds. On the other hand, an innovative coverage control algorithm combined with a probability hypothesis density (PHD) filter for target estimation is derived to settle detection and tracking tasks simultaneously. Both algorithms are analysed and discussed mathematically, with simulation experiments demonstrating their efficacy and performance. It is concluded that both algorithms solve the MR-MTT problem in terms of optimal coverage and optimal target estimation, respectively.