On-line analytical processing (OLAP) typically involves complex aggregate queries over large datasets. The data cube has been proposed as a structure that materializes the results of such queries in order to accelerate OLAP. A significant fraction of the related work has been on Relational-OLAP (ROLAP) techniques, which are based on relational technology. Existing ROLAP cubing solutions mainly focus on "flat" datasets, which do not include hierarchies in their dimensions. Nevertheless, as shown in this paper, the nature of hierarchies introduces several complications into the entire lifecycle of a data cube including the operations of construction, storage, indexing, query processing, and incremental maintenance. This fact renders existing techniques essentially inapplicable in a significant number of real-world applications and mandates revisiting the entire cube lifecycle under the new perspective. In order to overcome this problem, the CURE algorithm has been recently proposed as an efficient mechanism to construct complete cubes over large datasets with arbitrary hierarchies and store them in a highly compressed format, compatible with the relational model. In this paper, we study the remaining phases in the cube lifecycle and introduce query-processing and incremental-maintenance algorithms for CURE cubes. These are significantly different from earlier approaches, which have been proposed for flat cubes constructed by other techniques and are inadequate for CURE due to its high compression rate and the presence of hierarchies. Our methods address issues such as cube indexing, query optimization, and lazy update policies. Especially regarding updates, such lazy approaches are applied for the first time on cubes. We demonstrate the effectiveness of CURE in all phases of the cube lifecycle through experiments on both real-world and synthetic datasets. Among the experimental results, we distinguish those that have made CURE the first ROLAP technique to complete the construction and usage of the cube of the highest-density dataset in the APB-1 benchmark (12 GB). CURE was in fact quite efficient on this, showing great promise with respect to the potential of the technique overall. © Springer-Verlag 2009.