In this thesis, wetting properties of liquid droplets on micro and nano filaments were explored. First, droplet-on-filament systems were considered, made of liquid droplets and wetting between parallel filaments of identical geometries and surface wetting properties. Criteria for morphology transition between barrel-shaped droplet and droplet-bridge morphology was determined in terms of critical droplet volume at varying filament spacing, droplet volume, and contact angle. A family of wetting characteristic curves was obtained as a universal law of morphology transition in such systems. Additionally, wetting lengths of the above droplet-on-filament systems were demonstrated at varying geometries and surface properties. Secondly, a surface finite element method was employed to simulate the capillary torque generated in a droplet bridge formed between two misaligned filaments at varying filament spacing, contact angle, droplet volume, and filament orientation angle. Consequently, a novel, hydroelastic model was developed to examine the capillary effect in the mechanical response of ultrathin, soft filaments wetted with droplets and subjected to axial stretching. The filament was modeled as a hyperelastic, MooneyRivlin solid, and an explicit stress-stretch relationship was determined. The results obtained in this research broaden the theoretical understanding of droplet wetting and spreading on filaments and are applicable for design and analysis of filament-based microfluidic devices, biological cell manipulators, drug delivers, fiber wetting property differentiators, etc.