Computational continua is a higher order continuum formulation. From a theoretical point of view, the computational continua is endowed with fine-scale details; it introduces no scale separation; and makes no assumption about infinitesimality of the fine-scale structure. From computational point of view, the computational continua does not require higher order continuity; introduces no new degrees-of-freedom; and is free of higher order boundary conditions. The two salient features are: (i) the nonlocal quadrature scheme and reduced order homogenization. The nonlocal quadrature scheme, which replaces the classical Gauss (local) quadrature, allows for nonlocal interactions to extend over finite neighborhoods and thus introduces nonlocality into the two-scale integrals employed in various homogenization theories. The reduced order homogenization permits solution of complex nonlinear unit cell problems at a fraction of computational required by direct computational homogenization .