The article discusses different types of exotic options traded in the market. They are classified into two categories: path-independent options and path-dependent options. Path-independent options depend only on the final value of the underlying asset, while path-dependent options also consider its trajectory. Examples of path-independent options include forward start, binary, and compound options. Path-dependent options include barriers, lookbacks, and options on averages. The article focuses on mathematical models to value these options, aiming to find closed formulas for their valuation.