  We present a systematic way to derive the four-dimensional effective theories
for warped compactifications with fluxes and branes in the ten-dimensional type
IIB supergravity. The ten-dimensional equations of motion are solved using the
gradient expansion method and the effective four-dimensional equations of
motions are derived by imposing the consistency condition that the total
derivative terms with respect to the six-dimensional internal coordinates
vanish when integrated over the internal manifold. By solving the effective
four-dimensional equations, we can find the gravitational backreaction to the
warped geometry due to the dynamics of moduli fields, branes and fluxes.
