The Trojan Horse Method (THM) represents an indirect path to determine the bare nucleus astrophysical S-factor for reactions among charged particles at astrophysical energies. This is achieved by measuring the quasi-free cross section of a suitable three-body process. The method is also suited to study neutron-induced reactions, especially in the case of radioactive ion beams. A comprehensive review of the theoretical as well as experimental features behind the THM is presented here. An overview is given of some recent applications to demonstrate the method's practical use for reactions that have a great impact on selected astrophysical scenarios. Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 71 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.