This chapter shows how to recover the system's model itself based on the known relation between the input and output of a system. It discusses the realizability of weighting patterns. The chapter provides necessary and sufficient conditions and analyzes the uniqueness of the realization. In the case of time-invariant systems, it addresses the problem of realizability in a different way. The chapter presents methods to find a realization with minimal dimensional state variable, and, in addition, presents necessary and sufficient conditions to determine whether a given realization is minimal or not. The chapter provides necessary and sufficient conditions for the realizability of a given transfer function. Then, it discusses the minimal realizations. The chapter presents some real-life applications of the realization theory. It introduces methods that can be used to determine whether a realization of a given weighting pattern has minimal state dimension or not.