Multi-object systems are complex dynamical systems characterized by a varying number of objects and states that evolve randomly over time. These systems arise in diverse application domains, including multi-agent systems, surveillance, computer vision, robotics, and machine learning. The traditional State Space Model (SSM) fundamental to systems theory is not adequate to address key multi-object system problems such as state estimation, system identification, and control. This presentation introduces a generalized SSM based on the Labeled Random Finite Set (LRFS) framework. Contrary to the traditional SSM, a time sequence of states in a multi-object system does not necessarily represent the system trajectory. The LRFS framework, however, enables a time sequence of multi-object states to represent the multi-object system trajectory, which accommodates trajectory crossings, fragmentations, ancestries for spawning objects, and characterization of the uncertainty on the ensemble of objects (and their trajectories). The discussion will delve into cutting-edge tools for multi-object estimation and control, along with exciting applications, including autonomous vehicles, drones, computer vision systems, and large-scale multi-object tracking.