Recent innovations in genetics and imaging are providing the means to reconstruct cell lineages, either by tracking cell divisions using live microscopy, or by deducing the history of cells using molecular recorders. A cell lineage on its own, however, is simply a description of cell divisions as branching events. A major goal of current research is to integrate this description of cell relationships with information about the spatial distribution and identities of the cells those divisions produce. Visualising, interpreting and exploring these complex data in an intuitive manner requires the development of new tools. Here we present CeLaVi, a web-based visualisation tool that allows users to navigate and interact with a representation of cell lineages, whilst simultaneously visualising the spatial distribution, identities and properties of cells. CeLaVi's principal functions include the ability to explore and manipulate the cell lineage tree; to visualise the spatial distribution of cell clones at different depths of the tree; to colour cells in the 3D viewer based on lineage relationships; to visualise various cell qualities on the 3D viewer (e.g. gene expression, cell type, tissue layer) and to annotate selected cells/clones. All these capabilities are demonstrated with four different example data sets. CeLaVi is available at http://www.celavi.pro.