We discuss the formation and evolution of boxy/peanut bulges (B/Ps) and present new simulations results. Orbital structure studies show that B/Ps are parts of bars seen edge-on, they have their origin in vertical instabilities of the disc material and they are somewhat shorter in extent than bars. When the bar forms it is vertically thin, but after a time of the order of a Gyr it experiences a vertical instability and buckles. At that time the strength of the bar decreases, its inner part becomes thicker, so that, seen edge-on, it acquires a peanut or boxy shape. A second buckling episode is seen in simulations with strong bars, accompanied by a further thickening of the B/P and a weakening of the bar. Quantitatively, this evolution depends considerably on the properties of the halo and particularly on the extent of its core. This influences the amount of angular momentum exchanged within the galaxy, emitted by near-resonant material in the bar region and absorbed by near-resonant material in the halo and in the outer disc. Haloes with small cores generally harbour stronger bars and B/Ps and they often witness double buckling.