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We document our tomographic method and present a new global model of three‐dimensional (3‐D) variations in mantle P wave velocity. The model is parameterized by means of rectangular cells in latitude, longitude, and radius, the size of which adapts to sampling density by short‐period (1 Hz) data. The largest single data source is ISC/NEIC data reprocessed by Engdahl and coworkers, from which we use routinely picked, short‐period P , P g, Pn , pP , and pwP data (for earthquakes during the period 1964∼2007). To improve the resolution in the lowermost and uppermost mantle, we use differential times of core phases ( PKP AB − PKP DF , PKP AB − PKP BC , P diff − PKP DF ) and surface‐reflected waves ( PP‐P ). The low‐frequency differential times ( P diff , PP ) are measured by waveform cross correlation. Approximate 3‐D finite frequency kernels are used to integrate the long‐period data ( P diff , PP ) and short‐period ( P , pP , PKP ) data. This global data set is augmented with data from regional catalogs and temporary seismic arrays. A crust correction is implemented to mitigate crustal smearing into the upper mantle. We invert the data for 3‐D variations in P wave speed and effects of hypocenter mislocation subject to norm and gradient regularization. Spatial resolution is ∼100 km in the best sampled upper mantle regions. Our model, which is available online and which will be updated periodically, reveals in unprecedented detail the rich variation in style of subduction of lithospheric slabs into the mantle. The images confirm the structural complexity of downwellings in the transition zone discussed in previous papers and show with more clarity the structure of slab fragments stagnant in the transition zone beneath east Asia. They also reveal low wave speed beneath major hot spots, such as Iceland, Afar, and Hawaii, but details of these structures are not well resolved by the data used.