When does a satellite knot fiber?

Necessary and sufficient conditions are given for a satellite knot to be fibered. Any knot $\tilde{k}$ embeds in an unknotted solid torus $\tilde{V}$ with arbitrary winding number in such a way that no satellite knot with pattern $(\tilde{V},\tilde{k})$ is fibered. In particular, there exist nonfibered satellite knots with fibered pattern and companion knots and nonzero winding number.