The aim of this thesis is to contribute in the calculation of variational optical flow methods. This is a basic topic in the field of computer vision that pursues the accurate estimation of the displacement experienced by the objects present in a video scene. In particular, this dissertation is focused on two main themes: (i) we study the influence of temporal information compared to traditional spatial variational methods; (ii) we analyze several strategies for the preservation of flow discontinuities and propose alternatives to overcome this problem. Nowadays, these two issues remain unsolved and we consider them important for finding better optical flow fields. According to the enormous increment of the automation in the industry, the use of artificial intelligence and computer vision techniques in particular becomes more important. In this context, it is relevant to find automatic and well founded numerical methods to interpret moving scenes from image sequences. The document is divided in five chapters. In the first chapter we introduce the problem and give a guideline of this document. In the second, we study the most relevant works from the state-of-the-art that fits with the problems that we are dealing. Besides, we present several issues closely related with the context of this thesis, like standard datasets for optical flow studies or reproducible research. In the third chapter, we propose a spatio-temporal variational method for the consistent estimation of large motion fields. Our focus is on the development of realistic temporal coherence models that are suitable with current spatial models. The aim of this work is to explore ways of temporal coherence that takes into account the non-continuity of large motion fields. In this sense, we propose three main contributions: (i) a nonlinear flow constancy assumption, similar to the nonlinear brightness constancy assumption, (ii) a nonlinear temporal regularization approach; (iii) an anisotropic diffusion operator based on the Nagel-Enkelmann operator. The chapter four presents an implementation of the spatial and temporal approaches of the Brox et al. method and compare their main features. We also study various solutions using grayscale and RGB images from recent evaluation datasets to verify the color benefits in motion estimation. Finally, we analyze several strategies for the discontinuity-preserving problem in variational methods. Our analysis includes the use of tensors based on decreasing functions, which has shown to provide good results. We observe that this strategy is normally unstable if the function is not well controlled introducing instabilities in the computed motion field. Our conclusions lead us to propose two alternatives to overcome these drawbacks: (i) a simple approach that combines the decreasing function with a minimum isotropic smoothing; (ii) a fully automatic strategy that adapts the diffusion depending on the image features. It looks for the best parameter configuration that preserves the important motion contours and avoid instabilities. Our contributions have been tested on standards benchmark databases that are in common use in optical flow