In this paper, we present an OLAP framework for trajectories of moving objects. We introduce a new operator GROUP_TRAJECTORIES for group-by operations on trajectories and present three implementation alternatives for computing groups of trajectories for group-by aggregation: group by overlap, group by intersection, and group by overlap and intersection. We also present an interactive OLAP environment for resolution drill-down/roll-up on sets of trajectories and parameter browsing. Using generated and real life moving data sets, we evaluate the performance of our GROUP_TRAJECTORIES operator. An implementation of our new interactive OLAP environment for trajectories can be accessed at http://OLAP-T.cgmlab.org .