Two fundamental questions in the mechanics and physics of fracture are: (i) What is the relation between observable features of a material's microstructure and its resistance to crack growth? and (ii) What is the relation between observable features of a material's microstructure and the roughness of the fracture surface? An obvious corollary question is: What is the relation, if any, between a material's crack growth resistance and the roughness of the corresponding fracture surface? In 1984, Mandelbrot and co-workers showed that fracture surfaces exhibit self-affine, fractal-like scaling properties. This observation, together with advances in image analysis, precipitated a significant body of work in the physics community on the quantitative characterization of fracture surface roughness with the aim of relating the fractal dimension to crack growth resistance. While this effort was not successful, it raised the question of what measure, if any, of fracture surface roughness can be related to crack growth resistance. I will describe work on modeling ductile fracture that reveals a measure of the statistics of fracture surface roughness that can be quantitatively related to crack growth resistance and how this quantity relates to a measurable and (hopefully) controllable microstructural feature. Simulation results for two idealized microstructures will be discussed: one microstructure involves crack growth through a distribution of second phase particles and the other involves crack growth along grain boundaries. The implications for designing material microstructures with improved crack growth resistance will be discussed.