There are three practical challenges surrounding impulse drive design: acceleration, time dilation and energy conservation. In the show, inertial dampers compensate for acceleration. These hypothetical devices would have to be set so that the propellant retained its inertia after leaving the craft otherwise the drive would be ineffective. Time dilation would become noticeable at appreciable fractions of the speed of light. Regarding energy conservation, the television series and books offer two explanations:
Star Trek: The Next Generation Technical Manual indicates that the impulse engines are nuclear fusion engines where the plasma from the fusion reactor powers a massive magnetic coil to propel the ship. It is a form of magnetohydrodynamic or magnetoplasmadynamic thruster. This is used in conjunction with the ship's warp drive's alteration of the ship's relativistic mass, to achieve mid-to-high sub-light speeds. Thrusters, on the other hand, are closer to the designs of a high-efficiency reactant propellant (i.e. a sophisticated rocket engine) and are usually used for high-precision maneuvers. Ion propulsion drives are explicitly detailed to be used in Star Trek by Dominion and Iconian Starships and facilities.
Since a ship traveling at impulse velocities (slower than, but approaching, the speed of light) is still traveling in the normal space-time continuum, concerns of time dilation apply, and it is written in the ST:TNG Technical Manual that high relativistic speeds are avoided unless absolutely necessary; impulse power is therefore customarily limited to a maximum of 1⁄4 lightspeed. (Warp travel, on the other hand, is stated in the Manual to cause no kinds of time dilation effects.)