The focus of many particle tracking experiments in the last decade has been active systems, such as living cells. In active systems, the particles undergo simultaneous active and thermally driven transport. In contrast to thermally driven transport, particle motion driven by active processes cannot directly be correlated to the rheology of the probed region. The rheology in particle tracking experiments is typically obtained through the mean square displacements (MSD) of the trajectories. Hence, the MSD and its functional form remain the only basic tools to evaluate and compare living cells or other active systems. However, the mechano-structural characteristics of the intracellular environment and the mechanisms driving particle transport cannot be revealed by the MSD alone. Hence, approaches for advanced analysis of particle trajectories have been introduced recently. Here, we present a broad review of the extensive intracellular particle tracking experiments that have been carried out on a wide variety of cell types. Those works utilize the MSD, revealing similarities and differences relating to cell type and experimental setup. We also highlight several advanced trajectory-and displacement-based analysis methods and illustrate their capabilities using particle tracking data obtained from two cancer cell lines. We show that combining these analysis methods with the MSD can reveal additional information on intracellular structure and the existence and nature of active processes driving particle motion in cells.