To make contact with the physics of quarks, leptons, gauge fields and Higgses, this chapter presents a discussion of the pure supergravity Lagrangian of the graviton and gravitino to include couplings to these ‘matter fields’. The locally supersymmetric Lagrangian for the supergravity multiplet was derived from the globally supersymmetric Lagrangian using the Noether procedure. The chapter uses the same technique to illustrate how couplings of the supergravity multiplet to matter fields may be obtained. Whereas in globally supersymmetric theories supersymmetry breaking manifested itself in the appearance of a massless Goldstone fermion, in locally supersymmetric theories it was found that the corresponding effect is the appearance of a mass for the gravitino, which is the gauge particle of local supersymmetry. The simplest matter field system to couple to supergravity by making the supersymmetry local is the free massless chiral supermultiplet of the Wess–Zumino model.