We present a detailed study of the magnetic structure and spin waves in the Fe jarosite compound KFe3(SO4)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 et al. for various model Hamiltonians which include, in addition to isotropic Heisenberg exchange interactions between nearest (J1) and next-nearest (J2) 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 Kagomé plane. A brief discussion of how representation theory restricts the allowed magnetic structure is also given.