Perfect hash functions can potentially be used to compress data in connection with a variety of data management tasks. Though there has been considerable work on how to construct good perfect hash functions, there is a gap between theory and practice among all previous methods on minimal perfect hashing. On one side, there are good theoretical results without experimentally proven practicality for large key sets. On the other side, there are the theoretically analyzed time and space usage algorithms that assume that truly random hash functions are available for free, which is an unrealistic assumption. In this paper we attempt to bridge this gap between theory and practice, using a number of techniques from the literature to obtain a novel scheme that is theoretically well-understood and at the same time achieves an order-of-magnitude increase in performance compared to previous ``practical'' methods. This improvement comes from a combination of a novel, theoretically optimal perfect hashing scheme that greatly simplifies previous methods, and the fact that our algorithm is designed to make good use of the memory hierarchy. We demonstrate the scalability of our algorithm by considering a set of over one billion URLs from the World Wide Web of average length 64, for which we construct a minimal perfect hash function on a commodity PC in a little more than 1 hour. Our scheme produces minimal perfect hash functions using slightly more than 3 bits per key. For perfect hash functions in the range $\{0,...,2n-1\}$ the space usage drops to just over 2 bits per key (i.e., one bit more than optimal for representing the key). This is significantly below of what has been achieved previously for very large values of $n$.