This paper summarises some of the recent progress that has been made in understanding astrophysical plasma turbulence in the solar wind, from in situ spacecraft observations. At large scales, where the turbulence is predominantly Alfvénic, measurements of critical balance, residual energy and three-dimensional structure are discussed, along with comparison to recent models of strong Alfvénic turbulence. At these scales, a few per cent of the energy is also in compressive fluctuations, and their nature, anisotropy and relation to the Alfvénic component is described. In the small-scale kinetic range, below the ion gyroscale, the turbulence becomes predominantly kinetic Alfvén in nature, and measurements of the spectra, anisotropy and intermittency of this turbulence are discussed with respect to recent cascade models. One of the major remaining questions is how the turbulent energy is dissipated, and some recent work on this question, in addition to future space missions which will help to answer it, are briefly discussed.