This book gives an overview of cutting theories. It starts with a generic model, which is valid for all types of soil (sand, clay and rock) after which the specifics of dry sand, water saturated sand, clay, rock and hyperbaric rock are covered. For each soil type small blade angles and large blade angles, resulting in a wedge in front of the blade, are discussed. The failure mechanism of sand, dry and water saturated, is the so called Shear Type. The failure mechanism of clay is the so called Flow Type, but under certain circumstances also the Curling Type and the Tear Type are possible. Rock will usually fail in a brittle way. This can be brittle tensile failure, the Tear Type, for small blade angles, but it can also be brittle shear failure, which is of the Shear Type of failure mechanism for larger blade angles. Under hyperbaric conditions rock may also fail in a more ductile way according to the Flow Type of failure mechanism. For each case considered, the equations/model for the cutting forces, power and specific energy are given. The models are verified with laboratory research, mainly at the Delft University of Technology, but also with data from literature.