During growth processes many biological and physiological systems develop residual stresses. These stresses are present in the body even in the absence of external or body loadings and are known to play an important role in regulation processes. Residual stress can be observed when the body is cut and part of the stresses are relieved. A fundamental difficulty in elasticity is to describe the mechanics of a body with residual stresses. The problem comes from the absence of an obvious choice for an unstressed reference configuration where all kinematic and physical variables can be evaluated. By proper consideration of the manner in which stresses are relieved, one can define a virtual configuration. By borrowing arguments from elasto-plasticity and the theory of dislocations, the geometry of this configuration can be fully characterized. The virtual configuration is, in general, not a Euclidean manifold. It is associated with a metric (the growth metric) and an affine connection. These geometric objects shed some new light on some of the fundamental assumptions of the theory of growing elastic bodies. It also provides a theoretical framework to compute physical quantities of importance and help us understand the role of stresses in the mechanics of biological structures.