A Temporal database is one that supports some aspect of time distinct from user defined time. Over the last two decades interest in the field of temporal databases has increased significantly, with contributions from many researchers. However, the lack of efficient access methods is perhaps one of the reasons why commercial RDBMS vendors have been reluctant to adopt the advances in temporal database research. Therefore, an obvious research question is: can we develop more robust and more efficient access methods for temporal databases than the existing ones? This thesis attempts to address this question, and the main contributions of this study are summarised as follows: We investigated different representations of 'now' and how the modelling of current time influences the efficiency of accessing 'now relative' temporal data. A new method, called the 'Point' approach, is proposed. Our approach not only elegantly models the current time but also significantly outperforms the existing methods. We proposed a new index structure, called a Virtual Binary tree (VB-tree), based on spatial representation of interval data and a regular triangular decomposition of this space. Further, we described a sound and complete query algorithm. The performance of the algorithm is then evaluated both asymptotically and experimentally with respect to the state-of-the-art in the field. We claim that the VB-tree requires less space and uses fewer disk accesses than the currently best known structure - the RI-tree.