This chapter explores the theoretical foundations and formulation of Continuum-Kinematics-Inspired Peridynamics (CPD), a recent paradigm in strongly nonlocal (integral-type) elasticity. CPD modifies and extends classical peridynamics by incorporating the pertinent kinematic measures of continuum mechanics, enabling, for example, accurate modelling of the Poisson ratio, among other attractive features. The governing equations of CPD are achieved via a variationally consistent procedure at large deformations. CPD offers a robust framework to capture the nonlocal behaviour of materials. Due to its inherent integral format, CPD naturally accommodates discontinuities and is therefore as well suited to describe fracture. Admissible stored energy densities of CPD are outlined whereby in the limit of infinitesimal affine deformations their relationship to classical linear elasticity is established.