Spin relaxation parameters, although difficult to interpret, are attracting interest in NMR as these parameters are capable of yielding both structural and dynamic information. Cross-relaxation and cross-correlation parameters afford a non-ambiguous approach to molecular structure and dynamics although they require some special skills for their experimental determination and for their exploitation. This work will start with an introduction to nuclear spin cross-relaxation and cross-correlation phenomena in liquids then look in more detail at molecules in soft matter and large biomolecules. Providing a detailed, timely account, the authors are filling a gap in the present NMR literature for the analytical scientist.