As the sizes of modern datasets grow, many classical algorithms become prohibitively expensive, as the input is often too large to be stored in the memory of a single compute node. Streaming algorithms are designed to handle massive inputs using limited space: they process a stream of data items 'on the fly' while maintaining a small memory footprint at all times. In this talk I will discuss classical techniques for solving basic statistical estimation problems (e.g., moment estimation, distinct elements) on data streams, as well as recent results on graph analysis in the streaming model.