Abstract Time-lapse microscopy is a principal tool to unravel the mystery of how cells form and maintain organisms. The complexity of the domain of cellular dynamics demands a conceptual architecture as a solid theoretical foundation that supports the integration of knowledge obtained across experiments and theories. In this work, we outline the ontological foundation of cellular genealogies, a key concept for describing and representing of cellular development. We build the conceptual framework following the onto-axiomatic method: We first analyse the domain within the context of a top-level ontology (GFO). The resulting domain-specification provides the basis for a conceptualisation where we introduce concepts and relations. From these conceptualisations, we then construct model-structures adhering to the principles of model-theory. We finally elaborate axioms based on these model-structures. The developed framework provides the fundamental concepts underlying a Cell Tracking Ontology (CTO) that supports extraction and integration of biological knowledge from systems-level experiments across different types of observations at the single-cell level.