The design of the roof of the Olympic Stadium in Munich between 1969 and 1972 prompted H.J. Schek and K. Linkwitz to develop the force density method to determine the shape of large 3D cable nets in equilibrium between tensile cable forces and external loads. Given force densities, unconstrained form finding is a linear problem, which explains the great success of the method. As Schek had already noted, any extension of the formulation, e.g., by adding constraints, makes the problem nonlinear. Among other things, this was an important motivation that has since inspired much subsequent research. We will introduce the so-called revised force density method. It is derived consistently from the energy functional of the element forces, the external load, and the completely nonlinear kinematics, which is controlled by the force densities as methodological parameters. Consequently, we can formulate and efficiently solve a variety of problems to find the shape of 3D cable nets and lattice shells. This includes many constraints of practical importance and takes into account mixed tensile and compressive forces of hybrid and tensegrity structures. We can identify pre-stress forces and cutting lengths in goal-oriented shape optimization or determine the dual force diagrams of graphic statics by inverse force densities. We will also show how to generalize the force densities of cables to equivalent terms of membrane surfaces. We will carefully present the theory and formulation and demonstrate the performance and general success of the force density method using a variety of examples.