In this talk, we present and analyse a system of partial differential equations using the phase-field methodology to unravel the dynamics of tumor growth. For the first time, we integrate a phenotypic description into the framework. Phase-field models of tumor growth have proven useful as theoretical tools with which to investigate cancer invasion. However, a key implicit assumption underlying mathematical models of this type that have been considered so far is that cells in the tumor are identical. However, this assumption ignores the fact that cells in the same tumor may express different characteristics to different extents, exhibiting heterogeneous phenotypes, as well as the fact that cells may undergo phenotypic changes, with their characteristics evolving over time. To address this limitation, we incorporate intercellular phenotypic heterogeneity and the evolution of cell phenotypes into the phase-field modeling framework for the first time. This is achieved by formulating a phenotype-structured phase-field model of nutrient-limited tumor growth. A well-posedness result is established for this model under general assumptions on the model functions, covering a broad range of biologically relevant scenarios. To better elucidate the effect of phenotypic heterogeneity on tumor evolution, we propose numerical simulations based on a finite element approach.