The statistical properties of simple (complete) randomization, permuted-block (or simply blocked) randomization, and the urn adaptive biased-coin randomization are summarized. These procedures are contrasted to covariate adaptive procedures such as minimization and to response adaptive procedures such as the play-the-winner rule. General recommendations are offered regarding the use of complete, permuted-block, or urn randomization. In a large double-masked trial, any of these procedures may be acceptable. For a given trial, the relative merits of each procedure should be carefully weighed in relation to the characteristics of the trial. Important considerations are the size of the trial, overall as well as within the smallest subgroup to be employed in a subgroup-specific analysis, whether or not the trial is to be masked, and the resources needed to perform the proper randomization-based permutational analysis.