Criminology over the past 100 years can be criticized in general for barely increasing our ability to explain crime. However, this general criticism glosses over significant differences between what Robert Merton identified as low-, middle and high-range theories. Low-range theories are can be described as 'empirical laws', while high-range theories are are grand unifying concepts. Middle-range theories are principles--perhaps law-like statements in themselves--that aggregate empirical laws and are subsumed by high-range theories. This paper surveys explanation at each of these levels and argues that we do quite well with explanation at the scale of empirical laws, but still struggle with grand unifying concepts. Mathematics has the greatest potential to contribute in framing middle-range theory, which we can hope will make high-range theory more tractable.