Fixed point theorems are the most important tools for proving the existence and the uniqueness of the solutions to various mathematical models (differential, integral and partial differential equations and variational inequalities etc.), representing phenomena arising in different field such as steady state temperature distribution, chemical reactions, Neutron transport theories, economic theories, epidemic and flow of fluids. We can define fixed point as a point which remains invariant under the given transformation. The theory of fixed points is one of the basic tools to handle various physical formulations. Fixed point theorems in fuzzy mathematics are emerging with vigorous hope and vital trust. Here we reflect some light on the applications and developments of important branches of fixed point theory in fuzzy field.