Simulation wins where formulas run out. Path-dependent payoffs, multiple underlyings, stochastic volatility and barrier features are all easy to write as a simulation and impossible to express in closed form. The cost is computation and the fact that the answer carries statistical noise that shrinks only with the square root of the number of paths.
Early exercise is the awkward case, since a simulation runs forward and exercise decisions look backward. Specialised techniques exist, but for plain American equity options a binomial-model is simpler and faster.
Example: pricing a structure that pays based on XYZ's average price over 90 days. No formula applies. Simulate 200,000 paths from $50 with 25% volatility, compute each path's average, apply the payoff, discount the mean. Repeat with a different seed to see how much noise remains.
Related: binomial-model, black-scholes-model, embedded-option, theoretical-value