In a chemical rocket, the kinetic energy of the propellant is obtained from chemical bonds by burning the fuel. The available energy per unit mass is limited to about 10 MJ/kg, which limits the effective exhaust velocity to about 4.5 km/s. Nuclear reactions, on the other hand, can release the much larger binding energy between nucleons, of order 10^8 MJ/kg, implying effective exhaust velocities of around 0.05 c. In this chapter we look at the basics of nuclear fission and fusion, including reactors and the optimal reactions for propulsion. We then examine the various ways in which these can be used to propel a rocket, which includes both sustained reactions and miniature explosions. Although nuclear-propelled rockets have not been used in space (as far as we know), there has been quite some research and development. We will also look at the principles of antimatter propulsion and see what effective exhaust velocity this could achieve.