  We present a formalism for continuum and line emission from random clumpy
media together with its application to problems of current interest, including
CO spectral lines from ensembles of clouds and radio emission from HII regions,
supernovae and star-forming regions. For line emission we find that the effects
of clump opacity on observed line ratios can be indistinguishable from
variations of intrinsic line strengths, adding to the difficulties in
determining abundances from line observations. Our formalism is applicable to
arbitrary distributions of cloud properties, provided the cloud volume filling
factor is small; numerical simulations show it to hold up to filling factors of
about 10%. We show that irrespective of the complexity of the cloud ensemble,
the radiative effect of clumpiness can be parametrized at each frequency by a
single multiplicative correction to the overall optical depth; this multiplier
is derived from appropriate averaging over individual cloud properties. Our
main finding is that cloud shapes have only a negligible effect on radiation
propagation in clumpy media; the results of calculations employing point-like
clouds are practically indistinguishable from those for finite-size clouds with
arbitrary geometrical shapes.
