A major effort is being undertaken to sequence an array of mammalian genomes. Coincidentally, the evolutionary relationships of the 18 presently recognized orders of placental mammals are only just being resolved. In this work we construct and analyse the largest alignments of amino acid sequence data to date. Our findings allow us to set up a series of superordinal groups (clades) to act as prior hypotheses for further testing. Important findings include strong evidence for a clade of Euarchonta+Glires (=Supraprimates) comprised of primates, flying lemurs, tree shrews, lagomorphs and rodents. In addition, there is good evidence for a clade of all placental mammals except Xenarthra and Afrotheria (=Boreotheria) and for the previously recognised clades Laurasiatheria, Scrotifera, Fereuungulata, Ferae, Afrotheria, Euarchonta, Glires, and Eulipotyphla. Accordingly, a revised classification of the placental mammals is put forward. Using this and molecular divergence-time methods, the ages of the superordinal splits are estimated. While results are strongly consistent with the earliest superordinal divergences all being >65 mybp (Cretaceous period), they suffer from greater uncertainty than presently appreciated. The early primate split of tarsiers from the anthropoid lineage at ~55 mybp is seen to be an especially informative fossil calibration point. A statistical framework for testing clades using SINE data is presented and reveals significant support for the tarsier/anthropoid clade, as well as the clades Cetruminantia and Whippomorpha. Results also underline our thesis that while sequence analysis can help set up hypothesised clades, SINEs obtainable from sequencing 1-2 MB regions of placental genomes are essential to testing them. In contrast, derivations suggest that empirical Bayesian methods for sequence data may not be robust estimators of clades. Our findings, including the study of genes such as TP53, make a good case for the tree shrew as a closer relative of primates than rodents, while also showing a slower rate of evolution in key cell cycle genes. Tree shrews are consequently high value experimental animals and a strong candidate for a genome sequencing initiative.