  Formulating quantum integrability for nonultralocal models (NM) parallel to
the familiar approach of inverse scattering method is a long standing problem.
After reviewing our result regarding algebraic structures of ultralocal models,
we look for the algebra underlying NM. We propose an universal equation
represented by braided Yang-Baxter equation and able to derive all basic
equations of the known models like WZWN model, nonabelian Toda chain, quantum
mapping etc. As further useful application we discover new integrable quantum
NM, e.g. mKdV model, anyonic model, Kundu-Eckhaus equation and derive SUSY
models and reflection equation from the nonultralocal view point.
