This book provides the reader with a background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for advanced undergraduate or graduate students with a firm background in stochastics. Alongside the theoretical foundation, ready-to-implement algorithms and many examples make this book a valuable tool for anyone who is applying the methodology. General Introduction to Copulas; Univariate Sampling Schemes; Introduction to Monte Carlo Techniques; Elliptical Copulas; Archimedean Copulas; Marshall-Olkin Copulas; Pair-Copula Construction; Applications.