Altenkirch, Thorsten. Extensional Equality in Intensional Type Theory. [Link]
Hofmann, Martin. Conservativity of Equality Reflection over Intensional Type Theory. 1996. [Link]
Altenkirch, Thorsten McBride, Conor Swierstra, Wouter. Observational Equality, Now! [Link]
Identity Types
Dybjer, Peter. (What I Know about) the History of the Identity Type. [Link]
Homotopy Type Theory
Kraus, Nicolai. Equality in the Dependently Typed Lambda Calculus: An Introduction to Homotopy Type Theory. [Link]
Licata, Dan. Just Kidding: Understanding Identity Elimination in Homotopy Type Theory. [Link]
Writing tips:
How to write a literature review