The concept of function represents a major part of mathematics and becomes more significant in school during high school. Throughout history, it has been a difficult concept to define and may create challenges for contemporary students. This literature study aims to identify students' difficulties with the concept of function, as well as to account for how the definition of a function has evolved historically. The literature study has been conducted through database searches in ERIC, Education Research Complete and MathSciNet via EBSCOhost, as well as through chain searching. The study results in identifying that students' difficulties with the concept of function primarily include the graphical and algebraic forms of representation.