Broadcast Scheduling is a popular method for disseminating information in response to client requests. There are n pages of information, and clients request pages at different times. However, multiple clients can have their requests satisfied by a single broadcast of the requested page. In this article, we consider several related broadcast scheduling problems. One central problem we study simply asks to minimize the maximum response time (over all requests). Another related problem we consider is the version in which every request has a release time and a deadline, and the goal is to maximize the number of requests that meet their deadlines. While approximation algorithms for both these problems were proposed several years back, it was not known if they were NP-complete. One of our main results is that both these problems are NP-complete. In addition, we use the same unified approach to give a simple NP-completeness proof for minimizing the sum of response times. A very complicated proof was known for this version. Furthermore, we give a proof that FIFO is a 2-competitive online algorithm for minimizing the maximum response time (this result had been claimed earlier with no proof) and that there is no better deterministic online algorithm (this result was claimed earlier as well, but with an incorrect proof).