A laser thermal rocket uses the energy of a large remote laser, possibly ground‐based, to heat an inert propellant and generate thrust. Use of a pulsed laser allows the design of extremely simple thrusters with very high performance compared to chemical rockets. The temperatures, pressures, and fluxes involved in such thrusters (104K, 102atmospheres, 107w/cm2) typically result in the creation of laser‐supported detonation (LSD) waves. The thrust cycle thus involves a complex set of transient shock phenomena, including laser‐surface interactions in the ignition of the LSD wave, laser‐plasma interactions in the LSD wave itself, and high‐temperature nonequilibrium chemistry behind the LSD wave. The SDIO Laser Propulsion Program is investigating these phenomena as part of an overall effort to develop the technology for a low‐cost Earth‐to‐orbit laser launch system. We will summarize the Program’s approach to developing a high performance thruster, the double‐pulse planar thruster, and present an overview of some results obtained to date, along with a discussion of the many research question still outstanding in this area.