Fluorescence correlation spectroscopy (FCS) and fluorescence imaging have become very important tools for investigating molecular dynamics and molecular interactions in biological systems, especially in the intracellular environment. This dissertation focuses on both the development of FCS theory and methods and the application of FCS in studying protein dynamics in living cells. Fundamental theoretical treatments are presented regarding the effects of excitation saturation on FCS observation volume profiles, as well as detailed consideration of how objective lens fill factors influence volume profiles. We also consider theoretical models for anomalous diffusion in FCS, providing important clarification to the existing literature. We then discuss the use of FCS to study protein dynamics in living cells and demonstrate that the average mobility of biological molecules can be reliably characterized. The effects of different probe preparation methods on intracellular dynamics are also considered. The capability to apply FCS to investigate protein dynamics and interactions within living cells was exploited to investigate protein trafficking into the nucleus of eukaryotic cells. We present a comprehensive characterization of the intracellular mobility of nuclear import cargoes and receptors, and we show that these measurements have led to new insight into nuclear trafficking mechanisms in vivo.