Visually complex shapes with infinitesimally fine structure have for some time now been a topic of research for mathematicians. This thesis focuses on a particular type of fractals - IFS fractals which can be used to represent a variety of detailed self-similar shapes in nature, such as clouds, trees, mountains, sea shores, etc. We begin with a definition of fractals in the most general sense. We then move to iterated function systems (IFS). We define them, give a definition of IFS fractals, the most important examples and an algorithm for generating IFS fractals. Furthermore, we state Collage theorem which says that in order to find an IFS whose attractor ’resembles’ a given set, we need to aim to find a set of transformations whose union, that is, collage, of images of the given set is as close as possible to the given set. In the next section we introduce dynamical systems, their definition and some examples, and we connect them to iterated function systems. We give an algorithm for generating an orbit of dynamical systems, and also state the Shadowing theorem which is important in practice for calculating orbits of dynamical systems. Lastly, we cover iterated function systems with probabilities (IFSP). We define them, give examples of fractals generated with an IFS with probabilities as well as an algorithm for generating them. We state Elton’s theorem which formalizes our intuition about measure on fractals. We end the thesis with a theorem which illuminates the connection between IFS and IFSP.