Intense continua of electromagnetic radiation of very brief duration are formed in the interaction of focused ultra-short terawatt laser pulses with matter. Two different kinds of experiments, which have been performed utilizing the Lund 10 Hz titanium-doped sapphire terawatt laser system are being described, where visible radiation and X-rays, respectively, have been generated. Focusing into water leads to the generation of a light continuum through self-phase modulation. The propagation of the light through tissue was studied addressing questions related to optical mammography and specific chromophore absorption. When terawatt laser pulses are focused onto a solid target with high nuclear charge Z, intense X-ray radiation of few ps duration and with energies exceeding hundreds of keV is emitted. Biomedical applications of this radiation are described, including differential absorption and gated-viewing imaging.