Researchers in the field of quantum error correction (QEC) are primarily focussed on the development of approaches to overcome fundamental obstacles associated with physical implementations of quantum computing. QEC theory has evolved over the past decade from a collection of seminal examples and techniques, to a larger collection of seminal examples and techniques. In other words, much progress has been made, but there is still much to do. As the field has developed, it has also become apparent that there are links with other disciplines in quantum information science, such as quantum cryptography and quantum gravity. I’ll begin this talk by reviewing the basic mathematical framework for QEC. Then I’ll describe some of my recent work that has been motivated by (and hopefully will soon motivate) experimental efforts in quantum computing. If time permits, I’ll also discuss some of the connections mentioned above.