By Braided Geometry I mean a sort of Noncommutative Geometry dealing with braidings, i.e. solutions to Quantum Yang-Baxter Equation. In a sense, it can be treated as a far generalization of super-theory. The main role in this Geometry is played by the so-called Reflection Equation Algebra. This algebra has many remarkable properties which will be discussed in my talk. First, I'll exhibit the Joseph's contribution to this area. Second, I'll describe the update situation. Also, I plan to demonstrate some possible applications to Physics.