FX options are fairly straightforward when it comes to modeling choices. The standard lognormal approach embodied in the Black-Scholes formula is generally used by all market participants. This is in contrast to markets such as interest rates, which tend to use a normal rather than lognormal distribution assumption. The formula for the Black-Scholes call price is shown here and the terms are the same as the ones you'll have seen for pricing equity options.

As with other markets which use Black-Scholes, the flawed assumptions in the model are corrected for by the use of a volatility smile, or skew, which amends the option price by specifying a certain volatility for each strike. The volatility smile where all vols for out-of-the-money options tend to be higher than the at-the-moneys is used to correct for the assumed volatility of volatility. The skew where vols will display a systematic bias to puts or calls is used to correct for the assumed correlation between spot and implied volatility. Of course, they also absorb any supply and demand imbalances coming from end user trading of options.