The near-Earth space is a unique laboratory to explore turbulence and energy dissipation processes in magnetized plasmas thanks to the availability of high quality data from various orbiting spacecraft, such Wind, Stereo, Cluster, Themis, and the more recent one, the NASA Magnetospheric MultiScale (MMS) mission. In comparison with the solar wind, plasma turbulence in the magnetosheath remains far less explored, possibly because of the complexity of the magnetosheath dynamics that challenges any "realistic" theoretical modeling of turbulence in it. This complexity is due to different reasons such as the confinement of the magnetosheath plasma between two dynamical boundaries, namely the bow shock and the magnetopause; the high variability of the SW pressure that "shakes" and compresses continuously the magnetosheath plasma; and the presence of large density fluctuations and temperature anisotropies that generate various instabilities and plasma modes. In this paper we will review some results that we have obtained in recent years on plasma turbulence in the SW and the magnetosheath, both at the Magneto-HydroDynamics (MHD) and the sub-ion (kinetic) scales, using the state of the art theoretical models and in-situ spacecraft observations. We will focus on three major features of the plasma turbulence, namely its nature and scaling laws, the role of small scale coherent structures in plasma heating, and the role of density fluctuations in enhancing the turbulent energy cascade rate. The latter is estimated using (analytical) exact laws derived for compressible MHD theories applied to in-situ observations from the Cluster and Themis spacecraft. Finally, we will discuss some current trends in space plasmas turbulence research and future space missions dedicated to this topic that are currently being prepared within the community.