Mitotic serine/threonine kinases that contributes to the regulation of cell cycle progression. Associates with the centrosome and the spindle microtubules during mitosis and plays a critical role in various mitotic events including the establishment of mitotic spindle; centrosome duplication; centrosome separation as well as maturation; chromosomal alignment; spindle assembly checkpoint; and cytokinesis. Required for initial activation of CDK1 at centrosomes. Phosphorylates numerous target proteins; including ARHGEF2; BORA; BRCA1; CDC25B; DLGP5; HDAC6; KIF2A; LATS2; NDEL1; PARD3; PPP1R2; PLK1; RASSF1; TACC3; p53/TP53 and TPX2. Regulates KIF2A tubulin depolymerase activity. Required for normal axon formation. Plays a role in microtubule remodeling during neurite extension. Important for microtubule formation and/or stabilization. Also acts as a key regulatory component of the p53/TP53 pathway; and particularly the checkpoint-response pathways critical for oncogenic transformation of cells; by phosphorylating and stabilizing p53/TP53. Phosphorylates its own inhibitors; the protein phosphatase type 1 (PP1) isoforms; to inhibit their activity. Necessary for proper cilia disassembly prior to mitosis. {ECO:0000269|PubMed:11039908; ECO:0000269|PubMed:11551964; ECO:0000269|PubMed:12390251; ECO:0000269|PubMed:13678582; ECO:0000269|PubMed:14523000; ECO:0000269|PubMed:14702041; ECO:0000269|PubMed:14990569; ECO:0000269|PubMed:15128871; ECO:0000269|PubMed:15147269; ECO:0000269|PubMed:15987997; ECO:0000269|PubMed:17125279; ECO:0000269|PubMed:17360485; ECO:0000269|PubMed:17604723; ECO:0000269|PubMed:18056443; ECO:0000269|PubMed:18615013; ECO:0000269|PubMed:19351716; ECO:0000269|PubMed:19357306; ECO:0000269|PubMed:19668197; ECO:0000269|PubMed:19812038; ECO:0000269|PubMed:20643351; ECO:0000269|PubMed:9606188}.