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ABSTRACT: Mechanisms for the coronal heating and the acceleration of the solar wind are still largely debated. The thorough study of the solar wind for the past 60 years has, however, motivated an important focus on Alfvén waves and turbulence. Moreover, alike many other astrophysical plasmas, the solar wind is subject to numerous instabilities that are directly related to the turbulent cascade and its observed properties. In this talk, I will review and discuss models for Alfvén wave propagation and turbulent cascade, which eventually leads to dissipation. I will show how turbulent transport models can explain the large scale properties of the solar wind measured by the Parker Solar Probe and Solar Orbiter. In the light of a recent study, we will see why a compressible process -the parametric decay instability- is essential to the generation of a turbulent power spectrum from a narrow band emission of Alfvén waves at the solar surface. Finally, I will discuss the role of another instability, the tearing mode, in the generation of density perturbations and flux ropes in the inner heliosphere.