We use Black-Scholes for European options (mainly index options) and call options on stocks, and Bjerksund-Stensland for American put options.
Most other websites only use the Black-Scholes model, which can misprice American-style puts.
Our upcoming paid plan will add a third model that handles dividends more accurately. Black-Scholes and Bjerksund-Stensland assume dividends are paid as a steady rate, which isn’t realistic for many dividend-paying stocks. The new model will use a finite-difference approach to capture the real impact of dividend dates.