Inflation is a phase of accelerated expansion, taking place at very high energy in the early Universe. During this epoch, inhomogeneities are generated on cosmological scales from the amplification of quantum fluctuations of the gravitational and matter fields, that are stretched to distances of astrophysical interest today. The energy scales involved during this early epoch are many orders of magnitude greater than those accessible in particle physics experiments. The early Universe is thus one of the most promising probes to test far beyond standard model physics. When inflation is embedded in high-energy theories (supersymmetry, super-gravity, string theory, etc), different inflationary scenarios emerge that lead to different observational predictions. Those can be tested against high-precision measurements of the cosmic microwave background temperature and polarisation anisotropies. I will review the current status of the numerous proposed models, and highlight those for which the data show the strongest preference.