The structure and scaling properties of inwardly curved polymer brushes, tethered under good solvent conditions to the inner surface of spherical shells such as membranes and vesicles, are studied by extensive molecular dynamics simulations and compared with earlier scaling and self-consistent field theory predictions for different molecular weights of the polymer chains N and grafting densities σg in the case of strong surface curvature, R-1. We examine the variation of the critical radius R*(σg), separating the regimes of weak concave brushes and compressed brushes, predicted earlier by Manghi et al. [Eur. Phys. J. E 5, 519-530 (2001)], as well as various structural properties such as the radial monomer- and chain-end density profiles, orientation of bonds, and brush thickness. The impact of chain stiffness, κ, on concave brush conformations is briefly considered as well. Eventually, we present the radial profiles of the local pressure normal, PN, and tangential, PT, to the grafting surface, and the surface tension γ(σg), for soft and rigid brushes, and find a new scaling relationship PN(R)∝σg 4, independent of the degree of chain stiffness.