A major goal in dislocation theory is the development of a coarse-grained method that would enable predictions of dislocation response without resolving the degrees of freedom of all the dislocations. While a number of possible coarse-grained theories have been proposed, all of these need information about structures at scales smaller than the coarse-graining volume. Here we present results from dislocation simulations that yield scaling relations with the hope that they can provide a framework for modeling the sub-scale dislocation structures and dynamics. For example, we show that dislocations have a self-similar (fractal) structure over wide range of stress/strain; dislocations move by means of avalanches that have power-law (self-organized critical) behavior; and the energy, order and noise all scale as powers of the density, with a welldefined balance between noise and order.