Abstract
Tumour microenvironment is characterised by heterogeneity at various scales: from various cell populations (immune cells, cancerous cells, ...) and various molecules that populate the microenvironment; to phenotype heterogeneity inside the same cell population (e.g., cancer cells with different phenotypes; immune cells with different phenotypes and different functions). Here, I will highlight a few single-scale and multi-scale mathematical modelling approaches, that include local and/or non-local interactions between cells. The models are aimed at shedding some light on the complex tumour roles of these immune cells with different phenotypes on the evolution of the tumour and tumour environment. In particular, computational approaches are used to propose new biological hypotheses on the potential role of macrophages with mixed phenotypes on the evolution of tumours.