This talk will focus on conjugacies between textile systems. Thus it will start by discussing what a textile system is and how it yields a two dimensional shift of finite type. Next, a splitting of a textile system will be defined and shown to yield a conjugate system. The main result is that all conjugacies between textile systems can be decomposed into texitle splittings, amalgamations, and shift inversions. The proof of this result will be indicated and matrix conditions will be briefly discussed.