Japanese startup PD Aerospace is working on a reusable space plane to be ready by 2023.
(PD Aerospace space plane video)
In order to reach space with a single engine, the world’s first pulse-detonation based engine capable of alternating between jet combustion and rocket combustion modes is under development.
Patent for an engine that switches between jet detonation and rocket detonation depending on surrounding atmospheric conditions was obtained.
Simplicity of mechanism, high load, and high efficiency of such engine allows improved reliability and reduced flight cost.
The engine can be restarted during return flight and landing, allowing the spacecraft to have standby and divertsion capabilities.
As far as I know, the earliest science fiction reference to a "space shuttle", a reusable ship that takes off from the surface of the earth to rendezvous with a ship or station in space is this one from Hell Ship of Space, a 1940 story by Frederic Arnold Kummer, Jr.:
Many of the passengers slept, some played cards, others discussed in an undertone what they planned when they reached their destination. Already the speedster was decelerating,although so far nothing was visible in the blue-black darkness.
Suddenly a mutter ran along the aisle. Faint, ridiculously small rocket blasts cut the gloom far ahead; a string of all but invisible lights,like a necklace of glowing beads. Clearer and clearer with each second they loomed, as the speedster raced toward them. The shape of a huge ship began to come into view; rows of lighted windows, the occasional thrust of a lazy rocket blast.
With consummate skill the speedster slid alongside the huge craft...
(Read more about the space shuttle)