Online algorithms deal with settings where the input data arrives over time and the current decision must be made by the algo- rithm without the knowledge of future input. In the last few years, the online primal-dual approach, pioneered by Buchbinder and Naor, has emerged as a very powerful and general method to systematically design and analyze online algorithms.

In this talk, I will give an overview of the method and show how it uni es and simpli es various previous results. I will also describe the recent successes of this approach in addressing some classic problems such as weighted paging and the randomized k-server problem. Finally, we will also see some recent extensions of the method.