In a large-scale distributed infrastructure, users and administrators typically desire to perform on-demand operations that act upon the most up-to-date state of the infrastructure. These on-demand operations range from monitoring the up-to-date machine properties in the infrastructure, to making Grid scheduling decisions for different tasks based on the current status of the infrastructure. However, the scale and dynamism present in the operating environment make it challenging to support these operations efficiently. This paper discusses several on-demand operations that we have been studying, challenges associated with them, and how to meet the challenges. Specifically, we build techniques for 1) on-demand group monitoring that allows users and administrators of an infrastructure to query and aggregate the up-to-date state of the machines (e.g., CPU utilization) in a group or multiple groups, 2) an on-demand Grid scheduling strategy that makes scheduling decisions based on the current availability of compute nodes, 3) another on-demand Grid scheduling strategy that chooses the best algorithm for the current input data set among multiple algorithms available. We also present our ongoing work.