Control of spontaneously emitted light lies at the heart of quantum optics. It is essential for diverse applications ranging from miniature lasers and light-emitting diodes, to single-photon sources for quantum information, and to solar energy harvesting. To explore such new quantum optics applications, a suitably tailored dielectric environment is required in which the vacuum fluctuations that control spontaneous emission can be manipulated. Photonic crystals provide such an environment: they strongly modify the vacuum fluctuations, causing the decay of emitted light to be accelerated or slowed down, to reveal unusual statistics, or to be completely inhibited in the ideal case of a photonic bandgap. Here we study spontaneous emission from semiconductor quantum dots embedded in inverse opal photonic crystals. We show that the spectral distribution and time-dependent decay of light emitted from excitons confined in the quantum dots are controlled by the host photonic crystal. Modified emission is observed over large frequency bandwidths of 10%, orders of magnitude larger than reported for resonant optical microcavities. Both inhibited and enhanced decay rates are observed depending on the optical emission frequency, and they are controlled by the crystals' lattice parameter. Our experimental results provide a basis for all-solid-state dynamic control of optical quantum systems.