Early embryogenesis of most metazoans is characterized by rapid and synchronous cleavage divisions. In Drosophila embryos, waves of activity of Cdk1, the main regulator of the cell cycle, are responsible for the synchronization of cell divisions. After reviewing the phenomenology, I shall discuss the dynamics of the Ginzburg–Landau model that captures the in vivo dynamics of Cdk1. The main feature of the corresponding potential is that it features a time-dependent component, which accounts for the growing level of Cdk1 activation across the cell cycle. Two distinct regimes result. The first regime is experimentally observed in mutants that alter the regulation of the mitotic switch. In the resulting quasi-adiabatic regime, waves reflect the classical physical mechanism of invasion by a stable state of a metastable one. Conversely, the quasi-adiabatic approximation is violated in wild-type embryos, where the observed waves reflect the sweeping of spatial gradients of the Cdk1 field by the time-dependent component of the potential. This alternative mechanism leads to wave-like spreading, which is faster and depends on the dynamic parameters differently than bistable waves. For instance, the latter scale as the square root of the Cdk1 molecular diffusivity and weakly depend on the amplitude of the noise, whilst the former scale as 3/4 and 1/2 powers, respectively. Theoretical predictions are supported by experiments that couple quantitative measurements of Cdk1 and genetic perturbations.