The last five decades of molecular and systems biology research have provided unprecedented insights into the molecular and genetic basis of many cellular processes. Despite these insights, however, it is arguable that there is still only limited predictive understanding of cell behaviours. In particular, the basis of heterogeneity in single-cell behaviour and the initiation of many different metabolic, transcriptional or mechanical responses to environmental stimuli remain largely unexplained. To go beyond the status quo, the understanding of cell behaviours emerging from molecular genetics must be complemented with physical and physiological ones, focusing on the intracellular and extracellular conditions within and around cells. Here, we argue that such a combination of genetics, physics and physiology can be grounded on a bioelectrical conceptualization of cells. We motivate the reasoning behind such a proposal and describe examples where a bioelectrical view has been shown to, or can, provide predictive biological understanding. In addition, we discuss how this view opens up novel ways to control cell behaviours by electrical and electrochemical means, setting the stage for the emergence of bioelectrical engineering.