In this paper, we will observe relations and functions. Firstly, we will define the concept of relations and give an example of the application of relations in everyday life. Afterwards, we will analyze the properties of relations both theoretically and practically - through examples. We will focus on equivalence relations and partial order relations that must satisfy certain properties. We will then observe what must be valid for a relation to be a total order relation. The concepts of inverse relation and composition of relations, which we will also get acquainted with, stand out as important concepts in Mathematics. Furthermore, the second part of the paper is based on the function as a special case of the relation. We will show that a function can be defined as both a functional and a total relation. Moreover, we will explain how we can use a vertical test to check whether a given curve is a graph of a function as well as study two important connections between functions (equality of functions and restriction). After that, we will define injection, surjection and bijection as important features of the function and a horizontal test as an easier way to check the injectivity of the function. We will also get acquainted with the composition of functions and inverse functions through claims and examples. At the very end we will observe the monotonicity, parity and periodicity of the function.