Hagfishes are an ancient group of bottom dwelling marine animals that are best known for their ability to very quickly produce large volumes of gill-clogging slime when they are attacked by predators such as sharks. In this talk, I will discuss some of the more biophysical aspects of our work on this intriguing material, and will address the following questions: How do cells within hagfish slime glands produce the silk like protein fibres that hold the slime together? What is the nature of the glue that is involved in the deployment of slime threads in seawater from a coiled state to an unraveled state? What is the nature of the mucin gel particles that form the slimy part of hagfish slime, and what mechanisms are responsible for their swelling and rupture in seawater? Is it possible to make an artificial analog of hagfish slime by mixing synthetic fibres and hydrogels? Lastly, I will discuss our biomimetic efforts to produce fibrous protein materials that are inspired by hagfish slime threads.