In mitosis, the spindle assembly checkpoint (SAC) monitors the formation of microtubule‐kinetochore attachments during capture of chromosomes by the mitotic spindle. Spindle assembly is complete once there are no longer any unattached kinetochores. Here, we will discuss the mechanism and key components of spindle checkpoint signalling. Unattached kinetochores bind the principal spindle checkpoint kinase monopolar spindle 1 (MPS1). MPS1 triggers the recruitment of other spindle checkpoint proteins and the formation of a soluble inhibitor of anaphase, thus preventing exit from mitosis. On microtubule attachment, kinetochores become checkpoint silent due to the actions of PP2A‐B56 and PP1. This SAC responsive period has to be coordinated with mitotic spindle formation to ensure timely mitotic exit and accurate chromosome segregation. We focus on the molecular mechanisms by which the SAC permissive state is created, describing a central role for CDK1‐cyclin B1 and its counteracting phosphatase PP2A‐B55. Furthermore, we discuss how CDK1‐cyclin B1, through its interaction with MAD1, acts as an integral component of the SAC, and actively orchestrates checkpoint signalling and thus contributes to the faithful execution of mitosis.