Direct numerical simulations have been performed to study the dynamics of isolated turbulent spots in compressible isothermal-wall boundary layers. Results of a bypass transition scenario at Mach 2, 4 and 6 are presented. At all Mach numbers the evolved spots have a leading-edge overhang, followed by a turbulent core and a calmed region at the rear interface. The spots have an upstream-pointing arrowhead shape when visualized by near-wall slices, but a downstream-pointing arrowhead in slices away from the wall. The lateral spreading of the spot decreases substantially with the Mach number, consistent with a growth mechanism based on the instability of lateral shear layers. Evidence for a supersonic (Mack) mode substructure is found in the Mach 6 case, where coherent spanwise structures are observed under the spot overhang region.