Significance Light–matter interaction lies at the heart of several fundamental phenomena and technological applications ranging from photosynthesis to lasers. Current approaches to control this interaction such as optical cavities, photonic crystals, and metamaterials either rely on frequency resonance mechanisms which limit the bandwidth or suffer from poor light-coupling issues. Here we report a class of artificial media: photonic hypercrystals to control light–matter interactions. Both bandwidth and outcoupling limitations are overcome using hypercrystals. This characteristic is demonstrated through simultaneous enhancement of spontaneous emission rate (20×) and outcoupling (100×) from quantum dots embedded in the hypercrystal. This platform for broadband control of light–matter interaction will push the boundaries of applications such as ultrafast light-emitting diodes, photovoltaics, and quantum informatics.