A great place to discuss space technology and specifically technologies to get to Mars, is NewMars. That's the forum of the Mars Society.
http://www.newmars.com/forums
There are several space propulsion concepts:
Nuclear thermal: use a nuclear reactor to heat liquid hydrogen to super-heated gas which is exhausted out a nozzle like chemical rocket exhaust.
NERVA: Nuclear Engine for Rocket Vehicle Applications. They developed it at Jackass Flats, where the US military tested nuclear bombs. It worked, and the test facility is still there (although it has 1972 technology). The rocket was debugged and fine tuned. The first prototype had a problem with hypervelocity exhaust shaking the engine apart. They got that fixed and developed the engine so the next test would be in space. Then in 1972 it was cancelled along with the rest of the Apollo program. Nixon redirected funds from NASA to the Vietnam War. NERVA had a specific impulse (fuel efficiency) of 825 seconds. That means one pound of fuel will produce one pound of thrust for 825 seconds. In 1991 they upgraded the design and did computer simulations rather than a physical prototype, they got it up to 925 seconds. DARPA did a study, developed Timberwind based on a pebble bed reactor, they got it up to 1,000 seconds and the weight of the reactor was a lot less. Specifically, the mass of Timberwind 250 was 8,300kg with 250,000kgf thrust, NERVA2 massed 8,500kg with 34,000kgf thrust. To compare apples-to-apples, Timberwind 45 was a smaller version 45,000kgf thrust from engine mass 1,500kg. A significant improvement, but analysis of Timberwind showed the fuel elements would melt together, so it was a use-once only engine. NERVA could be restarted multiple times and plenty of extra power for electricity generation.
As a comparison, the main engine of the Space Shuttle was the most efficient chemical rocket engine at the time it was built. It produces 453 seconds in vacuum. There's now a LOX/LH2 engine that can produce 481 seconds, but it only works in vacuum, won't work at sea level or any atmospheric pressure at all. That gives you an idea how efficent the nuclear engines are.
gas core nuclear thermal
Use a vortex of gassified uranium with liquid hydrogen run down the middle of the vortex. The vast majority of uranium would circulate, but fission fragments (nuclear waste) would be included in the exhaust. Definitely for in-space use only. Direct contact from actively fissioning uranium with liquid hydrogen is the most efficient heat transfer. This is a very efficient engine design. Radiation is way, WAY, too much for use in Earth's atmosphere, but in space that radiation is like a teaspoon of water added to the ocean. The problem is how to test it? A solid core nuclear rocket contains the reactor in solid fuel elements so everything is contained, easy to test at Jackass Flats. But how would you test a GCNR? How do you develop a rocket that spews nuclear radiation? Consequently there hasn't been any serious work on it.
ion engines
Very high fuel efficiency but very low thrust. The idea is to slowly build speed. Great if you're not in a hurry, like an unmanned probe. A trip out to Pluto could result in reduced trip time since it could build so much speed, but for a trip to Mars you would get there before building significant speed; it would take more time than other propulsion systems.
hall effect
Similar to ion engines, same efficiency and propulsion, but uses a different principle of physics.
MPD: magnetoplasmadynamic
Almost as efficient as ion or hall, but a simpler design and can use hydrogen instead of xenon gas.
microwave water (I forget the name)
Medium thrust, medium fuel efficiency, uses water as propellant.
VASMR: Variable Specific impulse Magnetoplasma Rocket
Uses a slightly different principle of physics, but basically uses radio waves to heat liquid hydrogen similar to a microwave heating water. Contains the heated gas in a chamber for maximum pressure. Exhaust nozzle can be choked down for high pressure, producing low thrust but high fuel efficiency. Or openned for low pressure, high thrust but low fuel efficiency. Think of it as high gear and low gear for a rocket. Requires so much power that solar panels won't be enough, it needs a nuclear reactor. Uses liquid hydrogen as propellant, not xenon, so fuel is plentiful and cheap. Problem is the guy working on it still hasn't quite got it to work yet. At "high gear" the gas is so hot it would melt any known material so he uses a magnetic bottle. That leads to the same old problem of containing a high enough concentration of hot gas to be useful without leaking. Leakage could result in hot plasma touching the sides of the chamber, melting it.
Solar sail
A giant thin film of mylar, reflects light, uses light pressure for propulsion. Extremely low thrust but no propellant. Only works in the inner solar system, intensity of light outside the orbit of Mars is too low to produce any useful thrust.
MMPP: mini-magnetosphere plasma propulsion
A big magnet captures solar wind, uses that for propulsion. The magnet captures some ionized plasma, an electric current run through the plasma creates a bigger magnetic field, which captures more plasma, etc. There is a limit to how big the magnetosphere can inflate, the bigger the magnet the larger the maximum size of the magnetosphere. Also the closer to the sun the smaller the magnetosphere, due to solar wind stripping off loosely held plasma. But solar wind pressure is greater close to the sun. Total pressure from the sun remains the same from Mercury to Pluto, a slow but steady force. MMPP (or magnetic sail) provides more thrust than a solar sail (or light sail) but it requires significant power to run the electromagnets and electric current through the plasma.
Orion
Drop a series of nuclear bombs behind the spacecraft, with a concussion plate attached via shock absorbers to the spacecraft. Requires lifting hundreds of nuclear bombs in space (would other countries trust anyone who tried that?), and to work the spacecraft has to be inside the nuclear bomb's blast radius. Do you want to be that close to a nuclear bomb when it goes off?
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