  In this review paper, we illustrate a possible route to obtain a reliable
solution of the 2D Hubbard model and an explanation for some of the
unconventional behaviours of underdoped high-$T_\text{c}$ cuprate
superconductors within the framework of the composite operator method. The
latter is described exhaustively in its fundamental philosophy, various
ingredients and robust machinery to clarify the reasons behind its successful
applications to many diverse strongly correlated systems, controversial
phenomenologies and puzzling materials.
