The Big Bang Nucleosynthesis (BBN) model is a great success of nuclear astrophysics due to the outstanding agreement between observational and predicted light elements abundances. One exception, however, is the so-called "lithium problem." In this context, experimental efforts to measure the relevant reactions have been brought to an increased level of accuracy in measuring primordial abundances, and the introduction of indirect methods has allowed researchers to overcome the natural limitations of direct measurements in the energy range of interest for BBN. Here we review the results obtained from the application of the Trojan Horse Method to some of the most influential reactions of the standard network, such as 2 H(d,p) 3 H, 2 H(d,n) 3 He, 3 He(d,p) 4 He, 7 Li(p,α) 4 He, and 7 Be(n,α) 4 He. The relevant cross sections have been then used as new inputs to a classical BBN code, resulting in important constraints that make suggestions for a possible solution for the lithium problem outside of nuclear physics.