Reflection-Transmission Quantum Yang-Baxter Equations

We explore the reflection-transmission quantum Yang-Baxter equations, arising in factorized scattering theory of integrable models with impurities. The physical origin of these equations is clarified and three general families of solutions are described in detail. Explicit representatives of each family are also displayed. These results allow to establish a direct relationship with the different previous works on the subject and make evident the advantages of the reflection-transmission algebra as an universal approach to integrable systems with impurities.