This tutorial is available via youtube at https://youtu.be/zU-BRF6xLik. In this short course I will introduce branch point twist fields and explain how they emerge in the context of computing entanglement measures in 1+1D. I will focus on massive 1+1D integrable quantum field theory (IQFT) and also comment on some well-known results in conformal field theory (CFT). The talk will be structured into three main parts: First, I will introduce entanglement measures, focussing on the entanglement entropy, explain how these measures relate to partition functions in multi-sheeted Riemann surfaces and how these, in turn, may be expressed as correlators of branch point twist fields. Second, I will show how several well-known results in CFT and IQFT are very easily derived in this branch point twist field picture and how they can also be recovered numerically in a quantum spin chain. Finally, I will explain how more involved computations with branch point twist fields may be performed by exploiting form factor technology and will end the talk by showing an example of one such calculation.