The aim of this paper is to get acquainted with the basic concepts, theorems and results related to polynomial matrices. In the first chapter of the paper, a brief overview of matrices and polynomials is given, as an integral part of polynomial matrices, while in the second chapter we introduce the definition of polynomial matrices and basic operations on them. Moreover, the paper describes some important theorems, such as theorems related to the division of polynomial matrices, the small B`ezoute theorem and its generalization, and the Hamilton-Cayley theorem. Some examples and algorithms derived from the mentioned theorems are also attached. The terms: elementary transformation, linear independence and rank of polynomial matrices are also defined, which are actually analogous to those definitions in the classical vector space. The paper also deals with Smith’s canonical form of polynomial matrices and some results related to it. In addition, an algorithm for finding Smith’s canonical form is provided, which is supported by an example. One of the applications of polynomial matrices is explained in the last chapter. Accordingly, broadband systems with multiple inputs and multiple outputs, MIMO systems, in which the signal channel can be represented as a polynomial matrix, are briefly discussed. Besides, the definition of singular value decomposition is given, which is used when separating signals and evaluating the obtained information