Cell division, the purpose of which is to enable cell replication, and in particular to distribute complete, accurate copies of genetic material to daughter cells, is essential for the propagation of life. At a morphological level, division not only necessitates duplication of cellular structures, but it also relies on polar segregation of this material followed by physical scission of the parent cell. For these fundamental changes in cell shape and positioning to be achieved, mechanisms are required to link the cell cycle to the modulation of cytoarchitecture. Outside of mitosis, the three main cytoskeletal networks not only endow cells with a physical cytoplasmic skeleton, but they also provide a mechanism for spatio-temporal sensing via integrin-associated adhesion complexes and site-directed delivery of cargoes. During mitosis, some interphase functions are retained, but the architecture of the cytoskeleton changes dramatically, and there is a need to generate a mitotic spindle for chromosome segregation. An economical solution is to re-use existing cytoskeletal molecules: transcellular actin stress fibres remodel to create a rigid cortex and a cytokinetic furrow, while unipolar radial microtubules become the primary components of the bipolar spindle. This remodelling implies the existence of specific mechanisms that link the cell-cycle machinery to the control of adhesion and the cytoskeleton. In this article, we review the intimate three-way connection between microenvironmental sensing, adhesion signalling and cell proliferation, particularly in the contexts of normal growth control and aberrant tumour progression. As the morphological changes that occur during mitosis are ancient, the mechanisms linking the cell cycle to the cytoskeleton/ adhesion signalling network are likely to be primordial in nature and we discuss recent advances that have elucidated elements of this link. A particular focus is the connection between CDK1 and cell adhesion. This article is part of a discussion meeting issue 'Forces in cancer: interdisciplinary approaches in tumour mechanobiology'.