Within the geoscience community the estimation of natural resources is a challenging topic. The difficulties are threefold: Intitially, the design of appropriate models to take account of the complexity of the variables of interest and their interactions. This book discusses a wide range of spatial models, including random sets and functions, point processes and object populations. Secondly,the construction of algorithms which reproduce the variability inherent in the models. Finally, the conditioning of the simulations for the data, which can considerably reduce their variability. Besides the classical algorithm for gaussian random functions, specific algorithms based on markovian iterations are presented for conditioning a wide range of spatial models (boolean model, Voronoi tesselation, substitution random function etc.) This volume is the result of a series of courses given in the USA and Latin America to civil, mining and petroleum engineers, as well as to gradute students is statistics. It is the first book to discuss geostatistical simulation techniques in such a systematic way.