Slow dynamic processes, such as biomolecular folding/unfolding, macromolecular diffusion, etc., can be conveniently monitored by solution-state two-dimensional (2D) NMR spectroscopy, provided the inverse of their rate constants does not exceed the nuclear spin-lattice relaxation time constants (T1). The discovery of long-lived states (LLS) by Malcolm Levitt's group opened a new dimension for the study of slow dynamic phenomena, as magnetization stored in the form of LLS decays with the time constants TLLS, where in many cases TLLS >> T1. In this thesis, various excitation methods and applications of LLS are discussed. Broadband excitation of LLS is suitable to monitor slow processes and has been applied to study the slow ring-flip in tyrosine residues of BPTI (Bovine Pancreatic Trypsin Inhibitor), as well as to perform simultaneous measurements of diffusion coefficients in mixtures of molecules with arbitrary J-couplings and chemical shifts. The applications of LLS, initially believed to be limited to isolated spin-½ pairs, were extended to larger spin systems, including some common amino acids like Serine, Aspartic Acid, etc. LLS have been observed in Glycine residues of small peptides like Ala-Gly, as well as in mobile parts of proteins, e.g., in Gly 75 and 76 of Ubiquitin. The lifetimes TLLS are more sensitive to dipolar interactions with external spins than longitudinal and transverse relaxation time constants, T1 or T2, and therefore can provide structural information for unfolded proteins. The unfolding of Ubiquitin by addition of Urea and by varying pH was followed using LLS. The excitation of coherent superpositions across singlet and triplet states, which we call long-lived coherences (LLC's), leads to resolution enhancement in conventional NMR spectroscopy. New methods have been designed to store hyperpolarized (13C or 1H) magnetization in the form of LLS and have been demonstrated using samples of Ala-Gly and Acrylic Acid.