  We review the relation between the inflationary potential and the spectra of
density (scalar) perturbations and gravitational waves (tensor perturbations)
produced, with particular emphasis on the possibility of reconstructing the
inflaton potential from observations. The spectra provide a potentially
powerful test of the inflationary hypothesis; they are not independent but
instead are linked by consistency relations reflecting their origin from a
single inflationary potential. To lowest-order in a perturbation expansion
there is a single, now familiar, relation between the tensor spectral index and
the relative amplitude of the spectra. We demonstrate that there is an infinite
hierarchy of such consistency equations, though observational difficulties
suggest only the first is ever likely to be useful. We also note that since
observations are expected to yield much better information on the scalars than
on the tensors, it is likely to be the next-order version of this consistency
equation which will be appropriate, not the lowest-order one. If inflation
passes the consistency test, one can then confidently use the remaining
observational information to constrain the inflationary potential, and we
survey the general perturbative scheme for carrying out this procedure.
Explicit expressions valid to next-lowest order in the expansion are presented.
We then briefly assess the prospects for future observations reaching the
quality required, and consider a simulated data set that is motivated by this
outlook.
