As dividing cells transition into mitosis, hundreds of proteins are phosphorylated by a complex of cyclin-dependent kinase 1 (CDK1) and Cyclin-B, often at multiple sites. CDK1:Cyclin-B phosphorylation patterns alter conformations, interaction partners, and enzymatic activities and need to be recapitulated in vitro for the structural and functional characterization of the mitotic protein machinery. This requires a pure and active recombinant kinase complex. The kinase activity of CDK1 critically depends on the phosphorylation of a Threonine residue in its activation loop by a CDK1 activating kinase (CAK). We developed protocols to activate CDK1:Cyclin-B either in vitro with purified CDK1 activating kinases (CAK) or in insect cells through CDK-CAK co-expression. To boost kinase processivity, we reconstituted a tripartite complex consisting of CDK1, Cyclin-B, and CKS1. In this work, we provide and compare detailed protocols to obtain and use highly active CDK1:Cyclin-B (CC) and CDK1:Cyclin-B:CKS1 (CCC).