Boxy/peanut/X bulges, barlenses and the thick part of galactic bars: What are they and how did they form?

Bars have a complex three-dimensional shape. In particular their inner part is vertically much thicker than the parts further out. Viewed edge-on, the thick part of the bar is what is commonly known as a boxy-, peanut- or X- bulge and viewed face-on it is referred to as a barlens. These components are due to disc and bar instabilities and are composed of disc material. I review here their formation, evolution and dynamics, using simulations, orbital structure theory and comparisons to observations.