  Two types of Yang-Baxter systems play roles in the theoretical physics --
constant and colour dependent. The constant systems are used mainly for
construction of special Hopf algebra while the colour or spectral dependent for
construction of quantum integrable models. Examples of both types together with
their particular solutions are presented. The complete solution is known only
for the constant system related to the quantized braided groups in the
dimension two. The strategy for solution of the system related to quantum
doubles is suggested and partial results are presented.
