This thesis contains two components of research: studies of supercontinuum pulses generated in the novel microstructure fiber, and research on spatio-temporal coupling in ultrafast laser beams. One of the most exciting developments in optics in recent years has been the invention of the microstructure optical fiber. By controlling the structural parameters of these novel fibers in design and manufacturing, their dispersion profile can be freely tailored, opening up a huge application base. One particularly interesting effect in the microstructure fiber is the generation of ultrabroadband supercontinuum with only nJ-level Ti:sapphire oscillator pulse pump. This supercontinuum is arguably the most complicated ultrafast pulse ever generated, with its huge time-bandwidth product (> 1000 from a 16-cm-long fiber). Although many applications have been demonstrated or envisioned with this continuum, its generation is a very complicated process that is poorly understood, and the characteristics of the continuum pulses are not clearly known. In this work, we make a full-intensity-and-phase measurement of the continuum pulses using cross-correlation frequency-resolved optical gating (XFROG). The results reveal surprising unstable fine spectral structure in the continuum pulses, which is confirmed by single-shot measurements. Our study on the coherence of the continuum, on the other hand, shows that the spectral phase of the supercontinuum is fairly stable. Numerical simulations are carried out whose results are in good agreement with experiments. The second component of this thesis is the study of spatio-temporal coupling in ultrafast beams. We propose two definitions of spatial chirp, point out their respective physical meanings, and derive their relationship. On the common perception of the equivalence between pulse-front tilt and angular dispersion, we show that the equivalence only holds for plane waves. We establish a generalized theory of ultrafast laser beams with first-order spatio-temporal couplings, and discover a new pulse-front tilt effect associated with the combination of spatial chirp and temporal chirp. For the measurement of spatio-temporal distortions, the effects of such distortions in the input beam to a GRENOUILLE trace are carefully studied. An algorithm is proposed and tested to retrieve information about the distortions from the GRENOUILLE trace.