Transport processes occurring in the radiative interior of low-mass stars are evidenced by the surface variation of light elements, as well as by the evolution of the stellar rotation rate. While there are many independent transport models, there is a lack of self-consistent theories that permit stellar evolution models to simultaneously match the observations. The aim of the PhD thesis is to explore how additional transport processes can improve the agreement between models and observations. Using the code STAREVOL, we explored several transport processes for chemicals and for angular momentum. We identified the rotational dependence of the penetrative convection as a key process. Two additional parametric turbulent mixing processes are required to simultaneously explain the observed surface Li depletion (0.8-1.2 Msol) and the solar internal rotation profile. Finally, the Li-dip (1.3-1.5 Msol), displays a different trend, and a readjustment of the prescription and parameters are needed to reproduce it.