Though contact geometry is a venerable subject, beginning over two hundred years ago in the study of geometric optics, it has most recently moved to the foreground of mathematics. This is due largely to remarkable breakthroughs in the field over the last decade. Many of these advances have occurred by studying special knots related to contact geometry called Legendrian knots. I will indicate in my talk that those knots have connections to the deepest questions in contact geometry, however, I will focus on them as a subject unto themselves. Specifically, after recalling some basic facts from contact geometry, I will discuss what is known concerning their classification ("in the standard contact structure") in 3-space. If time permits I will describe various techniques currently being used to study Legendrian knots and some open problems.