As homework and other aspects of education migrate to a computer-based format, on-paper exams are beginning to seem like an anachronism. Online delivery is attractive, but comes with a myriad of implications not apparent at first glance. It affects the kinds of questions that can be asked and complicates administration of the exam, but it may make grading quicker. An online exam does not necessarily make cheating easier, though it demands new approaches to preventing cheating. An open-web exam is a special kind of online exam, in which students are allowed to use the Internet while taking the exam. It has its own set of advantages and disadvantages. For example, it provides a more authentic experience, but may make it hard to tell if students have done their own work. The authors report on a research study of online exams, based on the observations of hundreds of students and faculty who filled out two online surveys. Results will guide instructors in choosing the format that is right for their class.