This thesis deals with the derivation and travelling wave analysis of partial integro-differential equation models for EMT-mediated immunosuppression in cancer with phenotypic heterogeneity, including also the dynamics of killer and regulatory immune cells. Experimental evidence shows that mesenchymal cancer cells recruit regulatory cells, which suppress killer cell activity, creating a protective environment for the tumour. On the other hand, epithelial cancer cells experience higher immune activity due to the greater presence of killer cells. Cancer cells could have a phenotypic state ranging from totally epithelial to completely mesenchymal, modelled by the structure variable y. Specifically, a mesenchymal phenotype is characterized by high mobility and low proliferative ability, while an epithelial phenotype prioritizes reproduction over movement, reflecting the biological principle of “go or grow”.