Exotic options are options whose characteristics are more complex that those of regular (vanilla) options. What makes them special is the fact that different triggers may influence their payoffs, for example the average asset price over the time to expiry. They also may be based on some non-standard assets. The payoff of an exotic option does not necessarily depend on the entire path of the asset price, it can depend only on the asset price at expiry. The purpose of this paper is to provide a brief introduction to exotic options, with a focus on barrier options, lookback options and Asian options. Our focus is on calculating option prices in the Black-Scholes-Merton model. A barrier option is a type of financial derivative whose payoff depends on the asset price crossing over or falling below the pre-determined barrier. The payoff of a lookback option is based on the maximum value of the asset price. The payoff of an Asian option depends on the average asset price over the time to expiry and for such options, in general, there is no explicit formula for the option price. The price of an Asian option in the Black-Scholes-Merton model is determined through a partial differential equation. An example of pricing of an Asian option is demonstrated through Monte Carlo simulations in the R programming language.