Astronomy. What’s the first thing you think of when you read that word? The many beautiful vistas returned from Hubble? A family in a backyard huddled around a small telescope? Giant research observatories such as the Keck? Whatever may come to mind, it usually involves a telescope. But the very nature of telescopes has changed over the centuries, with different arrangements of lenses dominating for decades before succumbing to some combination of basic physics or technical limitations. We’ll (somewhat belatedly) celebrate the 400th anniversary of Galileo’s telescope by taking you on a quick tour of four centuries of progress and frustration.