Types of Rocket Propulsion and Potential Space Drives

There is lots of interest these days in space exploration. After fifty years we are looking at going back to the Moon to build a base and early planning for a manned trip to Mars.
After that, further exploration and settlement of the Solar System will be on the table.
One of the main limiting factors for all of this space exploration are the types of rockets and rocket engines available to get there.
Current rockets in usage are mainly chemical rockets with fairly low specific impulses. We wi...