Despite considerable progress on the information-theoretic broadcast channel, the capacity region of fading broadcast channels with channel state known at the receivers but unknown at the transmitter remains unresolved. We address this subject by introducing a layered erasure broadcast channel model in which each component channel has a state that specifies the received signal levels in an instance of a deterministic binary expansion channel. We find the capacity region of this class of broadcast channels. The capacity achieving strategy assigns each signal level to the user that derives the maximum expected rate from that level. The outer bound is based on a channel enhancement that creates a degraded broadcast channel for which the capacity region is known. This same approach is then used to find inner and outer bounds to the capacity region of fading Gaussian broadcast channels. The achievability scheme employs a superposition of binary inputs. For intermittent AWGN channels and for Rayleigh fading channels, the achievable rates are observed to be with 1-2 bits of the outer bound at high SNR. We also prove that the achievable rate region is within 6.386 bits/s/Hz of the capacity region for all fading AWGN broadcast channels.