Spatial and temporal dynamics of polymer chains play critical roles in their rheological properties, which have a significant influence on polymer processing and fabrication of polymer-based (nano) materials. Many theoretical and experimental studies have aimed at understanding polymer dynamics at the molecular level that give rise to its bulk phase properties. While much progress has been made in the field over the past ~60 years, many aspects of polymers are still not understood, especially in complicated systems such as entangled fluids and polymers of different topologies. In addition, the physical properties of biological macromolecules, i.e. DNA, are expected to affect the spatial organization of chromosome in a cell, which has the potential impact on a broad epigenetics research. Here, we propose new methods for simultaneous visualization of diffusive motion and conformational dynamics of individual polymer chains, two most important factors that characterize polymer dynamics, based on a new single-molecule tracking technique, cumulative-area (CA) tracking method. We demonstrate the applicability of the CA tracking to the quantitative characterization of the motion and relaxation of individual topological polymer molecules under entangled conditions, which is possible only by using the newly-developed CA tracking, using fluorescently-labeled linear and cyclic dsDNA as model systems. We further extend the technique to multi-color CA tracking that allows for the direct visualization and characterization of motion and conformation of interacting molecules. We also develop a new imaging method based on recently developed 3D super-resolution fluorescence microscopy technique, which allows direct visualization of nanoscale motion and conformation of the single molecules that is not possible by any other methods. Using these techniques, we investigate spatial and temporal dynamics of polymers at the single-molecule level, with special emphasis on the effect of topological forms of the molecules and the confined geometry on their spatiotemporal dynamics. Our results demonstrate that the new methods developed in this thesis provide an experimental platform to address key questions in the entangled topological polymer dynamics. The research will provide a platform for developing new polymer-based materials and open the possibility of studying spatial organization of DNA in a confined geometry from physics point of view.