Diffuse low-grade gliomas are slowly growing tumors. After tens of years, they transform inexorably into more aggressive forms, jeopardizing the patient’s life. Mathematical modeling could help clinicians to have a better understanding of the natural history of these tumors and their response to treatments. We present here different models of these tumors: the first one is discrete and describes the appearance of the first glioma cells and the genesis of a tumor. The second model is continuous and consists in a PDE that describes the evolution of the cell density. This model can describe the natural evolution of gliomas, their response to treatments such as radiotherapy and the changes in their dynamics in pregnant women. The discrete and the continuous models are designed to be close to the biological reality. The results are quantitatively compared with either biological data or clinical data, at the cellular level (histological samples) and at the tissue level (MRI scans).