This paper reviews some of the observational properties of globular cluster systems, with a particular focus on those that constrain and inform models of the formation and dynamical evolution of globular cluster systems. I first discuss the observational determination of the globular cluster luminosity and mass function. I show results from new very deep HST data on the M87 globular cluster system, and discuss how these constrain models of evaporation and the dynamical evolution of globular clusters. The second subject of this review is the question of how to account for the observed constancy of the globular cluster mass function with distance from the center of the host galaxy. The problem is that a radial trend is expected for isotropic cluster orbits, and while the orbits are observed to be roughly isotropic, no radial trend in the globular cluster system is observed. I review three extant proposals to account for this, and discuss observations and calculations that might determine which of these is most correct. The final subject is the origin of the very weak mass-radius relation observed for globular clusters. I discuss how this strongly constrains how globular clusters form and evolve. I also note that the only viable current proposal to account for the observed weak mass-radius relation naturally effects the globular cluster mass function, and that these two problems may be closely related.