Today’s enterprise computing architectures are characterized by a complex memory hierarchy: different application requirements in terms of latency, bandwidth, persistence, and access pattern, as well as characteristics of available memory and storage technology require combining different technologies. Building highly efficient data management and analytics solutions that meet the challenges of modern applications requires to utilize this memory hierarchy, i.e., taking the specific characteristics of a given technology into account and keeping data objects in the optimal level. In this paper, we present results of our project on exploiting modern memory hierarchies in support of hybrid transactional/analytical processing (HTAP) on graph data. First, we discuss the design and evaluation of data structures and query operations for graph data in persistent memory. Second, we present an approach to support the analysis of graph data on GPU-based accelerators with dedicated memory by efficient data transfer and consistency mechanisms. Finally, we propose a storage and processing strategy for (bi-)temporal graphs using temporal materialized views while exploiting the memory hierarchy.