The Li-S battery has been under intense scrutiny for over two decades, as it offers the possibility of high gravimetric capacities and theoretical energy densities ranging up to a factor of five beyond conventional Li-ion systems. Herein, we report the feasibility to approach such capacities by creating highly ordered interwoven composites. The conductive mesoporous carbon framework precisely constrains sulphur nanofiller growth within its channels and generates essential electrical contact to the insulating sulphur. The structure provides access to Li+ ingress/egress for reactivity with the sulphur, and we speculate that the kinetic inhibition to diffusion within the framework and the sorption properties of the carbon aid in trapping the polysulphides formed during redox. Polymer modification of the carbon surface further provides a chemical gradient that retards diffusion of these large anions out of the electrode, thus facilitating more complete reaction. Reversible capacities up to 1,320 mA h g(-1) are attained. The assembly process is simple and broadly applicable, conceptually providing new opportunities for materials scientists for tailored design that can be extended to many different electrode materials.