Theoretical methods for designing sequences of radio frequency (rf) radiation pulses for broadband excitation of spin systems in nuclear magnetic resonance (NMR) are described. The sequences excite spins uniformly over large ranges of resonant frequencies arising from static magnetic field inhomogeneity, chemical shift differences, or spin couplings, or over large ranges of rf field amplitudes. Specific sequences for creating a population inversion or transverse magnetization are derived and demonstrated experimentally in liquid and solid state NMR. One approach to broadband excitation is based on principles of coherent averaging theory. A general formalism for deriving pulse sequences is given, along with computational methods for specific cases. This approach leads to sequences that produce strictly constant transformations of a spin system. The importance of this feature in NMR applications is discussed. A second approach to broadband excitation makes use of iterative schemes, i.e. sets of operations that are applied repetitively to a given initial pulse sequences, generating a series of increasingly complex sequences with increasingly desirable properties. A general mathematical framework for analyzing iterative schemes is developed. An iterative scheme is treated as a function that acts on a space of operators corresponding to the transformations produced by all possible pulse sequences. …