Cold and ultracold molecules are highly desirable for a diverse range of applications in physics and chemistry such as precision measurements, tests of fundamental physics, quantum simulation and information processing, quantum chemistry, and the physics of strongly correlated quantum matter. Laser cooling is usually infeasible in molecules because their rotational and vibrational transitions make is difficult to come up with a closed scattering cycle. Recently, a narrow range of diatomic molecules, one of which is CaF, has been shown to possess a convenient electronic structure and a highly-diagonal Franck-Condon matrix and thus be amenable to laser cooling. This thesis describes experiments on laser cooling of CaF radicals produced in a supersonic source. We first investigate the increased fluorescence when multi-frequency resonant light excites the molecules from the four hyperfine levels of the ground X²Σ+(N = 1, v = 0) state to the first excited A²π½(J' = 1=2; v' = 0) state. The number of photons scattered per molecule increases significantly from one or two in the single frequency case to more than 50 before the molecules get pumped into the X²Σ+(N = 1; v = 1) state. We demonstrate laser cooling and slowing of CaF using counter-propagating laser light which causes the molecules to scatter more than a thousand photons on the X (N = 1, v = 0, 1) <->A (J' = 1=2; v' = 0) transition. The effect of the laser cooling is to slow a group of molecules from 600 ms-1 to about 580 ms-1 and to narrow their velocity distribution from an initial temperature of 3 K down to 300 mK. In addition, chirping the frequency of the cooling light to keep it on resonance with the decelerating molecules doubles the deceleration and further compresses the velocity distribution. The effect of the laser cooling is limited by the optical pumping of molecules in the X (N = 1, v = 2) state.