In three dimensions, a simplical piecewise-linear manifold is formed by joining flat Euclidean tetrahedra. The triangular faces that border two neighbouring tetrahedra are identified, so that the space formed by any pair of tetrahedra is also Euclidean. Curvature then arises when the developement of tetrahedra is continued around an edge, with the sum of the dihedral angles at the edge deviating from a full rotation by a A'deficit angleA'. These deficit angles are related to a projection of the Riemann curvature tensor, making local definitions of the Riemann and Ricci curvature tensors quite difficult. This talk will cover some recent work on relating the deficit angles to sectional curvature, and combining this with a piecewise-linear scalar curvature to give the a Ricci curvature in the direction of each edge. Potential extensions to higher dimensions will also be discussed.