Theoretical approaches to liquid Helium

In this article, we review the main theoretical methods applied to the study of liquid Helium adopting a microscopic approach, that is, starting from the many-particle Hamiltonian of the system. Following an introduction on the first early approaches, we discuss two main issues. In the first one, we report the main ingredients of a theoretical approach based on the variational method, with the discussion of the high accuracy obtained with them and the related progress in the design of highly accurate trial wave functions. In the second part, the main stochastic methods used in this study are briefly discussed. Altogether reflects the strong links between the study of liquid Helium and the progress in the development of new and extremely powerful approaches to deal with one of the most strongly quantum many-body systems in Nature.