In this thesis, compression of supercontinua generated using two fundamentally different techniques is studied. In one method, supercontinuum generation is achieved in gas-filled hollow-core fibers in the mJ pulse energy range, whereas the other technique exploits the nonlinearity of microstructure fibers using nJ pulses at the full oscillator repetition rate. Successful compression of broad supercontinua with mJ pulse energies is an important prerequisite for a number of fundamental experiments. For example, the generation of single attosecond pulses by high-order harmonic generation relies on the production of high-peak-power light pulses in the single-cycle regime. Compression of supercontinua generated using two hollow fibers in a cascading geometry led to the production of one of the shortest pulses ever obtained in the visible and near-infrared spectral region. The experiments performed on microstructure fibers in the nJ pulse energy range were divided in two pumping regimes (anomalous and normal dispersion). Since previous theoretical simulations suggested limitations concerning the compressibility of the generated supercontinua, additional numerical simulations of pulse propagation through these fibers have been performed. Pumping in the normal dispersion regime led in excellent agreement with the numerical simulations to the generation of the shortest pulses ever obtained using microstructure fibers. For the case of pumping in the anomalous dispersion regime however, the simulations suggest, that with today’s state-of-the-art pulse compressors a clean compression of the generated supercontinua is not possible.