Hybrid High-Order (HHO) methods are a class of new generation numerical schemes for PDEs with several advantageous features, including: (i) support of general polytopal meshes in arbitrary space dimension; (ii) arbitrary approximation order; (iii) compliance with the physics, including robustness with respect to the variations of physical coefficients and reproduction of key continuous properties at the discrete level; (iv) reduced computational cost thanks to hybridization, static condensation, and compact stencil. This presentation contains an introduction as well as examples of applications to nonlinear problems. [1] D. A. Di Pietro and A. Ern, A hybrid high-order locking-free method for linear elasticity on general meshes, Comput. Meth. Appl. Mech. Engrg., 2015, 283:1–21. DOI: 10.1016/j.cma.2014.09.009. [2] D. A. Di Pietro and R. Tittarelli, An introduction to Hybrid High-Order methods, arXiv preprint arXiv:1703.05136, March 2017. [3] D. A. Di Pietro and J. Droniou, A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes, Math. Comp., 2017. Published online. DOI: 10.1090/mcom/3180. [4] D. A. Di Pietro and J. Droniou, Ws,p-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems, Math. Models Methods Appl. Sci., 2017. Published online. DOI: 10.1142/S0218202517500191. [5] D. A. Di Pietro and S. Krell, A Hybrid High-Order method for the steady incompressible Navier–Stokes problem, arXiv preprint arXiv:1607.08159, July 2016.