Genome maps are crucial tools in human genetic research, providing known landmarks for locating disease genes and frameworks for large-scale sequencing. Radiation hybrid mapping is one technique for building genome maps. In this paper, we describe the methods used to build radiation hybrid maps of the entire human genome. We present the hidden Markov model that we employ to estimate the likelihood of a map despite uncertainty about the data, and we discuss the problem of searching for maximum-likelihood maps. We describe the graph algorithms used to find sparse but reliable initial maps and our methods of extending them. Finally, we show results validating our software on simulated data, and we describe our genome-wide human radiation hybrid maps and the evidence supporting them.