In recent years, several devices allow to measure real vector fields, leading to a better understanding of fundamental phenomena such as fluid dynamics or brain water movements. This gives vector field visualization and analysis new challenges in many applications in engineering and in medicine. In particular real data is generally corrupted by noise, puzzling the understanding provided by visualization tools. This data needs a denoising step as preprocessing, however usual denoising removes discontinuities and singularities, which are fundamental for vector field analysis. In this dissertation a novel method for vector field denoising based on random walks is proposed which preserves certain discontinuities. It works in a unstructured setting; being fast, simple to implement, and shows a better performance than the traditional Gaussian denoising technique. This dissertation also proposes a semi-automatic vector field denoising methodology, where the user visually controls the filtering scale by validating topological changes caused by classical vector field filtering.