Do any manufacturers have plans to use turbojets in future aircraft? What is the state-of-the-art in turbojet design?
The first jets were turbojets simply because the turbine could only support its own compressor. They kept an edge for supersonic flight and will be the engine of choice if we ever design another Mach 3+ aircraft. Also, micro jets for cruise missiles and model aircraft turbines are turbojets to keep them simple. However, the analysis of modern jet warfare showed that the overwhelming majority of flight time is spent at high subsonic speeds, and there a turbofan makes more sense.

Now all modern combat jet aircraft use turbofans, even though their bypass ratio is rather low (around 0.5).

Commercial jet transport engines are solidly turbofans since half a century and have slowly increased their bypass ratio to about 9, less for smaller engines. Now three-spool engines or geared turbofans are state of the art, because they allow more freedom in optimizing the rotation speed of the different sections inside the engine.

Turbojets have benefited from better, more heat-resistant materials and airfoils for turbo machinery just as much as turbofans, but modern designs are overwhelmingly turbofans, so turbojets generally represent a much earlier technological level. To give you an example: The first turbojet used in operation, the Jumo 004, had a mass of more than 700 kg and produced 8.8 kN of thrust. The engine of the Eurofighter, the EJ200, is only slightly bigger in mass and has similar dimensions, weighing 990 kg, but produces seven times the thrust of the Jumo 004. With reheat, thrust is more than 10 times that of the Jumo 004, which had no afterburner. The pressure ratio could be increased from 3.2 to 26 (that is the progress in compressor aerodynamics), and the turbine entry temperature from 840°K to 1800°K (that is the progress in materials).