The global properties of galaxies such as their observed luminosities may be severely affected by internal obscuration of the stars by dust. In this thesis I examine the amount and extent of this obscuration using the following approaches: For a sample of eight galaxies for which I have obtained multi-waveband optical and near-infrared observations I have investigated the reddening of individual regions, the optical depth inferred from hydrogen column densities (using an assumed gas to dust ratio) and the optical depth calculated using a detailed energy balance between the observed stellar and far infrared (FIR) fluxes. In addition I investigate the variation of the scale length of galaxies at different wavelengths and the variation of galaxies' blue magnitudes with inclination. I find that two of these tests which are sensitive to zeta, the relative vertical scale heights of the stars and dust, suggest that values of zeta >/= 0.5 are necessary to be consistent with the data. The observed B-band central optical depths of my sample are found to vary between ~2 and ~25. I suggest a value of ~8 ± 3 fora 'typical' spiral galaxy. Such a galaxy would be optically thick to beyond its half-light radius, and it would have an extinction of 0.75 mag (50% of the blue luminosity). However, uncertainties still remain as many of my conclusions are based on a small data set. More observations of a larger sample, together with observations beyond 100 microns, are required to solve this important problem.