In this talk, I will describe crosscap states in integrable field theories and spin chains in 1+1 dimensions. I will derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. I will then compute the crosscap entropy, i.e. the overlap for the ground state, in some examples. In the examples analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. I will discuss crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. I will comment on the realization of crosscap states in holography. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.