In 1967 Francis Crick and Sydney Brenner proposed that we need mathematical models of cells to understand their complexity and their behaviour; in 2001 mathematical modelling of cells was identified as a grand challenge of 21st Century science. In order to understand the complexity of life, in order to integrate and interpret experimental data, and in order to control cellular processes in biotechnology and synthetic biology we need a conceptual, analytical, and predictive framework – referred to as the CellMap by Sydney Brenner. I will discuss three facets, centred around cell differentiation and developmental process, of how we can start to distill “design principles” underlying cellular behaviour. Here design principles are understood as the essential properties that a system needs to possess to be able to fulfil certain functions. I will discuss the interplay of cell lineages, molecular networks, and phenotypic landscapes, their intricate interdependencies, and how they shape cell-fate decision making processes. These are, of course, only baby-steps towards Brenner’s dream of a CellMap, but taking them has already allowed us to map out and embark on a feasible path towards such models.