Monopropellants are chemicals that decompose all by themselves at a rate fast enough to be considered rocket propellants.
Hydrogen peroxide is first on the list. H2O2 in a high purity state will in the presence of a catalyst decompose (burn) at high temperature. It can also be used as an oxidizer and was used by the Germans during W.W.II in the ME163 rocket plane and as the turbopump gas generator in the V2 rocket. Some ME163 pilots died from hydrogen peroxide leaking into their cabin. ISP 170.
Hydrazine, N2H4, is used as a monopropellant in spacecraft thrusters. The thrusters are lined with catalyst to maintain combustion. I have been told that in engines over 15,000 # thrust it will burn all by itself. ISP 180.
Nitrous oxide, N2O, just misses the list of monopropellants. It contains only enough energy to burn slowly in the gaseous state when at high pressure.
The big problem with monopropellants is safety. If it will decompose all by itself in the combustion chamber, it may do so in the main propellant tank also = explosion.
Thermal engines. Hey, the idea is to produce hot gas right? The best gas is hydrogen of course, and you can heat it with a solar mirror, an electric arc, or a nuclear reactor. NASA put a lot of effort into the development of nuclear thermal engines in the 60's. The NERVA engine was test fired several times, but proved too "hot" to handle. The diameter of the Saturn V third stage was actually set by the design of a proposed nuclear engine. All thermal engines require huge amounts of energy which is their great drawback.
Ion. The true space engine. Now we are getting down to particle physics. Take an atom, cesium or mercury, strip off an electron to ionize it, then use electric and magnetic fields to accelerate it to relativistic velocities( a portion of the speed of light). It takes a lot of electrical power but you get an ISP of 3,000 to 10,000! Ion engines only work in a vacuum and at very low thrust levels (0.1 # or less). They have been tested in vacuum chambers for years, but only recently has a spacecraft been seriously proposed to use the engines in space. These simple engines have no moving parts and with a suitable power source can make crossing the great distances of interplanetary space practical. They run continuously for thousands of hours to build up tremendous velocities.
Warp drives. Sorry no one has invented a field drive engine yet. Would be nice though. Send working models to Mark Goll, 19785 Marbach Lane, San Antonio, Texas, 78266-2136.
Hybrids. I saved this one for last. A hybrid motor has a liquid propellant and a solid propellant. Liquid oxygen or liquid nitrous oxide are common oxidizers, and any solid that will burn is the common fuel. Everything from paper to plastic to rubber has been stuffed into hybrid motors. Hybrid engines are becoming very popular with amateurs and hobbyists. The fuel is formed into a tube lining the combustion chamber wall, with the oxidizer injected down the middle. The heat of the combustion chamber causes the fuel to vaporize at it's solid surface, the fuel vapors then mix with the oxidizer to burn, which produces more heat, etc.. The big plus for hybrids is that they are extremely safe and easy to handle. The big minus is poor performance and combustion instability. The problem is simple to demonstrate. There are two types of flame. Premixed as in the burners on your stove or furnace which produce hot smooth burning flames, and diffusion flames as in a candle which produces a smoky yellow flickering flame. Liquid bipropellant engines and solid propellant engines are examples of premixed flames, the fuel and oxidizer are mixed before they burn. The hybrid is an example of a diffusion flame, the fuel and oxidizer are separate and meet at the flame front. ISPs are low in hybrids, about 170, and they burn rough.