This talk will be on joint work with Robert Laugwitz and Milen Yakimov (arXiv:2307.14764) that is motivated by obtaining solutions to the quantum reflection equation (qRE). To start, given a braided monoidal category C and C-module category M, we introduce a version of the Drinfeld center Z(C) of C adapted for M. We refer to this category as the "reflective center" E_C(M) of M. Just like Z(C) is a canonical braided monoidal category attached to C, we show that E_C(M) is a canonical braided module category attached to M. We will also discuss the case when C is the category of modules over a quasitriangular Hopf algebra H, and show how quantum K-matrices arise in this setting (thus yielding solutions to the qRE).