When it comes to tools and techniques designed to help understanding complex abstract data, visualization methods play a prominent role. They enable human operators to leverage their pattern finding, outlier detection, and questioning abilities to visually reason about a given dataset. Many methods exist that create suitable and useful visual representations of static abstract, non-spatial, data. However, for temporal abstract, non-spatial, datasets, in which the data changes and evolves through time, far fewer visualization techniques exist. This thesis focuses on the particular cases of temporal hierarchical data representation via dynamic treemaps, and temporal high-dimensional data visualization via dynamic projections. We tackle the joint question of how to extend projections and treemaps to stably, accurately, and scalably handle temporal multivariate and hierarchical data. The literature for static visualization techniques is rich and the state-of-the-art methods have proven to be valuable tools in data analysis. Their temporal/dynamic counterparts, however, are not as well studied, and, until recently, there were few hierarchical and high-dimensional methods that explicitly took into consideration the temporal aspect of the data. In addition, there are few or no metrics to assess the quality of these temporal mappings, and even fewer comprehensive benchmarks to compare these methods. This thesis addresses the abovementioned shortcomings. For both dynamic treemaps and dynamic projections, we propose ways to measure temporal stability; we evaluate existing methods considering the tradeoff between stability and visual quality; and we propose new methods that strike a better balance between stability and visual quality than existing state-of-the-art techniques.