Optical waveguides provide rich environment for various nonlinear processes thanks to the long interaction lengths, sustained high intensities and diverse dispersion regimes. Nonlinear and dispersion properties of fibers and waveguides can be widely controlled through microstructuring resulting in a broad family of photonic crystal and bandgap waveguides. This flexibility can be used to realize previously impossible nonlinear interaction regimes for solitons and quasi-continuous waves. The dynamics of femtosecond optical pulses in such dispersive and nonlinear materials provide a truly challenging measurement task, but reward us with most spectacular images of nonlinear wave interactions. We visualized the dynamics of solitons and continua in several such structures using cross-correlation frequency-resolved optical gating, the technique which provides experimentally the most complete information about an optical pulse. These detailed time and frequency-resolved measurements infinitely surpass the simple spectral measurements or even the time axis-symmetric FROG spectrograms. Soliton dynamics in the vicinity of the second zero-dispersion point of a silica PC fiber, Cherenkov continuum generation, stabilization against the Raman self-frequency shift and other resonant interactions as well as the supercontinuum generation in soft-glass fibers were characterized. Recent theoretical studies were brought about to develop a fundamental understanding of these resonant interactions and excellent agreement was found.