Ways to compute Greeks from a pricer

You have a function that prices a derivative. What techniques can you use to get its Greeks, and what are the trade-offs?

Finite differences, pathwise derivatives, likelihood-ratio weights and adjoint (AAD) methods. Bump-and-reprice is generic but costs extra pricings and has bias and, under Monte Carlo, noise unless random numbers are reused. Pathwise differentiation is unbiased and low-variance but needs a smooth payoff. Likelihood-ratio handles discontinuous payoffs at the price of higher variance. AAD gives all sensitivities for a small multiple of one pricing but takes effort to implement.