Radiation hybrid (RH) mapping is a somatic cell method for obtaining ordering information of markers on a chromosome, using relatively few experiments. Given the results of a typical RH experiment, finding the true order of the markers is a challenging algorithmic problem. In this work we present several simple algorithms for ordering and mapping the markers, where the input is the genomic data obtained from RH experiments. We provide a rigorous analysis of these algorithms. In particular, we show that under the standard statistical model for RH, our algorithms are "statistically consistent." That is, given enough hybrids, the algorithms do reconstruct the true markers' order (with high probability). We also prove a simple lower bound for the number of hybrids required (by any algorithm) to correctly reconstruct the order. We have implemented these algorithms, and tested them on synthetic and real data. These simulations show that for practical input sizes (number of markers and hybrids) our algorithms produce outputs that are very close to the true ordering. The simulations also indicate that the true ordering of the markers is usually not the one which minimizes the number of obligate chromosome breaks.