  We present a detailed study of the magnetic structure and spin waves in the
Fe jarosite compound ${\rm KFe_3(SO_4)_2(OH)_6}$ for the most general
Hamiltonian involving one- and two-spin interactions which are allowed by
symmetry. We compare the calculated spin-wave spectrum with the recent neutron
scattering data of Matan {\it et al.} for various model Hamiltonians which
include, in addition to isotropic Heisenberg exchange interactions between
nearest ($J_1$) and next-nearest ($J_2$) neighbors, single ion anisotropy and
Dzyaloshinskii-Moriya (DM) interactions. We concluded that DM interactions are
the dominant anisotropic interaction, which not only fits all the splittings in
the spin-wave spectrum but also reproduces the small canting of the spins out
of the Kagom\'e plane. A brief discussion of how representation theory
restricts the allowed magnetic structure is also given.
