Autoignition plays a fundamental role in high-speed combustion systems, such as scramjet engines, where combustion occurs at large Karlovitz numbers and the turbulence can be highly compressible, with turbulence Mach numbers Mat textgreater 0.1. The effects of compressible turbulence on the ignition delay time and intermittency of autoignition in high-speed combustion are investigated here using direct numerical simulations of three-dimensional, reactive, homogeneous isotropic turbulence with single-step Arrhenius reaction kinetics. Probability distributions of the fuel massfraction and reaction rate reveal large increases in intermittency and small-scale structure between the linear and non-linear compressibility regimes, with eddy shocklets appearing at Mat textgreater 0.4. Detailed time histories of fluid parcel pathlines are analyzed in the Lagrangian reference frame for Mat = 0.2, 0.4, and 0.6. Results indicate that at the turbulence Mach numbers expected in scramjet engines, compressibility significantly shortens ignition delay time, and both subsonic and supersonic spontaneous autoignition waves can be formed simultaneously in both the linear and non-linear compressibility regimes.