Elastic Brownian filaments exhibit rich dynamics that are essential in numerous biological and industrial processes, such as intracellular transport and flagellar motion in biology, processing of rod-like polymers, and other rheological phenomena found in soft matter systems. Single filament scale research is needed to better understand these dynamics. One common theme governing these systems is non-linear dynamics as a result of the competition between the elastic and viscous forces acting on the filament, with thermal energy oftentimes adding stochasticity to the dynamics. This has resulted in behavior that cannot be simply explained by mechanical force balances. In this work, we investigate the two-dimensional dynamics of a semiflexible filament on the low-Reynolds number regime using experimental, theoretical and numerical methods. Experimentally, we synthesize DNA-linked superparamagnetic colloidal filaments and apply them as models for inextensible semiflexible filaments under various external fields. Theoretically, we utilize a worm-like chain model and slender-body theory to provide scaling and other analytical insights. A bead-spring chain model Brownian dynamics simulation is utilized to provide a numerical approach to support the experimental and theoretical results. Applying these methods, we study the model filament dynamics induced by two force fields: magnetic and gravitational fields. Firstly, the filament is induced to bend and buckle using an orthogonal magnetic field. The limits of linear elastic bending observed within an experimental regime is identified. Various non-linear dynamical stages leading to a higher-order filament buckling and configurational instabilities are examined. The inhomogeneous temporal evolution of the buckling wavelength is analyzed and the contractions under various conditions are compared. Secondly, a gravitational field is applied to semiflexible filaments. The configurational transitions and sediment dynamics of the model filament is studied in an otherwise quiescent fluid. The effect of thermal fluctuations on the stochasticity of the filament configurations and orientations is investigated. We also consider the settling dynamics of the semiflexible filament in more confined geometries, such as a post array, where interactions between the filament and post influence the migration path. This thesis advances our understanding of the multitude of configurations and non-linear dynamics of semiflexible colloidal filaments induced by external forces and under the influence of thermal fluctuations. This body of work will contribute to the development of novel soft materials as well as providing new insights of the properties of related filament systems.