A method for purification and separation of cannabinoids, such as cannabidiol and tetrahydrocannabinol, e.g., from the dried hemp and cannabis leaves can use a continuous simulated moving bed process and a combination of one or more of a sequence of purification steps including: filtration, decolorization, activation or decarboxylation, dewaxing, polishing, and crystallization to separate a cannabinoid from the cannabis plant and to provide various cannabinoid products. The cannabinoid products can be used in various pharmaceutical and nutraceutical applications.