Quantum computers are being developed across the world and they span multiple hardware technologies. However, a common critical problem for all of them is noise and decoherence. This makes quantum error correction a fundamental requirement to build scalable, fault-tolerant, quantum computers. In this talk I will introduce this exciting mathematical field and illustrate the key concepts. I will discuss the two interconnected requirements of quantum error correction: fast decoders to correct errors and fault-tolerant implementations of quantum logic on the information encoded into quantum error correcting codes. During these discussions, I will share results from my own work as well as others from the Arizona Quantum Initiative (AQuI) at the university (https://aqui.arizona.edu). I will also make connections to other applications of quantum error correction, such as in quantum networks being developed by our NSF Center for Quantum Networks (https://cqn-erc.org).