Optical caustics, bright features of focused light, have been known since the early days of physics history. Although originated in optics, caustics play an important role in many fields of physics such as radio frequency propagation, acoustics and gravitational lensing. Using Catastrophe Theory for analyzing caustics illuminates their universal properties. In this work, we show the role of caustics in high harmonic generation (HHG). The enhancement associated with caustics serves as an important key for controlling the HHG spectra. We demonstrate this ability by producing dramatic enhancements in the HHG spectrum, corresponding to a swallowtail caustic. Importing the caustics “toolbox” to HHG offers a deeper understanding of the process, pointing out the natural places where non-classical features appear.