We outline several methods for obstacle reconstruction from
far field scattering data, comparing and contrasting the strengths of
each. The first method
we discuss is a ``single wave" technique for determining the general
size and location of
scattering obstacles. Once we know where to look, we focus our
computational energy
into a local region, using multi-static/multi-frequency data to tease
out the shape of the scatterers. We
will compare several different ideas for accomplishing this ranging
from generalized
filtered backprojection to linear sampling. All of these methods are
so-called ``direct methods" -
no iterative refinement proceedure is used. We will discuss
advantages and disadvantages to these approaches.