We consider the no-flux initial-boundary value problem for the cross-diffusive evolution system which was introduced to describe the dynamics of urban crime.  In bounded intervals I will first discuss the existence of global classical solutions for all reasonably regular non-negative initial data. Next I will address the issue of determining the qualitative behavior of solutions.  Finally, I will conclude with some numerical simulations exploring possible effects that may arise when considering large cross diffusion terms not covered by our qualitative analysis.