Digital video content dominates the overall internet traffic in form of streaming or video telephony, which was especially observable during the shutdown due to the COVID-19 pandemic in the first half of the year 2020. Modern video coding standards, such as HEVC and VVC, rely on the hybrid video coding scheme, which combines the principle of a DPCM loop with transform coding, and was not changed over the last decades. However, data driven approaches have proven their potential in regard to classical inverse problems in image processing recently. In particular, the Sparse-Land signal model showed promising results for the problems of e.g. denoising and super-resolution. Therefore, the concepts of dictionary learning and sparse coding are reviewed in this work, and an improved patch combination method for dictionary learning-based super-resolution is presented. Moreover, this thesis builds on the conjecture that the application of pretrained sparse image models in the coding loop or in higher level coding concepts allows for compression rates which go beyond the performance of state-of-the-art video coding standards. Consequently, the main contribution of this work is the analysis of sparse signal models in the context of Versatile Video Coding (VVC). To this end, a sparse coding-based loop filter is proposed, dictionary learning-based super-resolution is introduced to several higher level coding concepts, and a sparse coding-based intra prediction method is developed. All approaches were evaluated experimentally and the reported results indicate their potential for a compression performance beyond video coding standards such as HEVC and VVC.