© 2018, Springer International Publishing AG, part of Springer Nature. In this chapter, we review some bifurcations exhibited by the classical Lorenz system, where the parameters can have any real value. Analytical results on the pitchfork, Hopf and Takens–Bogdanov bifurcations of the origin, as well as the Hopf bifurcation of the nontrivial equilibria, are summarized. These results serve as a guide for the numerical study that reveals other important organizing centers of the dynamics: Takens–Bogdanov bifurcations of periodic orbits, torus bifurcations and the resonances associated, homoclinic and heteroclinic connections with several degeneracies, etc. We also point out that the analysis of the Hopf-pitchfork and the triple-zero bifurcations of the origin cannot be performed with the usual tools and propose a way to carry out this study avoiding the structural singularities exhibited by the Lorenz system.