A (layered) broadcast approach is studied for fading wiretap channels. The basic idea is to employ superposition coding to encode information into a number of layers and use stochastic encoding for each layer to keep the corresponding information secret from an eavesdropper. The legitimate receiver successively decodes information one layer after another by canceling the interference caused by the layers that the receiver has already decoded. The advantage of this approach is that the transmitter does not need to know the channel states to the legitimate receiver and the eavesdropper, but can still securely transmit certain layers of information to the legitimate receiver. The layers that can be securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The Gaussian wiretap channel with fixed channel gains is first studied to illustrate the idea of the broadcast approach. Three cases of block fading wiretap channels with a stringent delay constraint are then studied, in which either the legitimate receiver's channel, the eavesdropper's channel, or both channels are fading. For each case, the secrecy rate that can be achieved by using the broadcast approach is obtained, and the optimal power allocation over the layers (or the conditions on the optimal power allocation) is also derived.