  We review a recent development in theoretical understanding of the quenched
averaged correlation functions of disordered systems and the logarithmic
conformal field theory (LCFT) in d-dimensions. The logarithmic conformal field
theory is the generalization of the conformal field theory when the dilatation
operator is not diagonal and has the Jordan form. It is discussed that at the
random fixed point the disordered systems such as random-bond Ising model,
Polymer chain, etc. are described by LCFT and their correlation functions have
logarithmic singularities. As an example we will discuss in detail the
application of LCFT to the problem of random-bond Ising model in $ 2 \leq d
\leq 4$.
