A review of a number of methods for random fields simulation in conjunction with Monte Carlo studies of probabilistic mechanics problems is presented from a broad perspective. This article complements some of the previous review articles in that it compares various simulation algorithms, assesses their relative computational efficiency and versatility, discusses the properties of generated field samples, and incorporates some of the recent developments. Collectively, a comprehensive discussion of the covariance decomposition method, the spectral method, the ARMA method, the noise shower method, the scale refinement methods, and the turning band method is attempted. For tutorial effectiveness univariate, uni-dimensional, Gaussian, and homogeneous fields are discussed, primarily in connection with various simulation methods. Nevertheless, appropriate references are included addressing the simulation of more general fields. This review article contains 110 references.