For a rocket
The problem with gaining high velocities is the rocket equation - the amount of fuel you need to carry grows exponentially (that's really, REALLY fast) for an increase in delta v (that's the difference between final and initial velocity).
With nuclear fuel you need millions of tonnes of fuel to reach a delta v of 0,2c (acceleration to 0,1c and deceleration to 0).
You can reach a delta v of 0,1c (final speed 0,05c) with a reasonable quantity of nuclear fuel, though - without a genius to change the paradigm, that's the maximum velocity theoretically possible with today's physics.
With chemical fuel -
Note: 0,1c is not even close to 0,7c , where relativistic mas increase actually becomes a problem.
We should be so lucky as to have only this problem.
For a laser/particle-beam sail technology
The laser emitter must be the size of Jupiter to counter diffraction. And it consumes an amount of energy comparable to burning through millions of tonnes of nuclear fuel in order to create enough photons for a delta v of 0,2c (photons are REALLY energy hungry momentum transfer instruments).
For warp drive:
Call me when you get exotic matter - and there are about half a dozen other unsolvable (currently) problems with it.