The observations of the 12 known magnetic white dwarfs are reviewed and a list of mechanisms is discussed which could give rise to the observed absorption and polarization spectra. Particular emphasis is placed on the observations of, and mechanisms important in the 3 magnetic white dwarfs to be modelled - BPM 25114, G 99-47 and GD 90. The calculation of continuum flux and polarization in these stars is discussed: the ATLAS computer programme (Kurucz,1970) is outlined and the linear theory of circular dichroism (Lamb and Sutherland,1974) is described together with its effects on radiative transfer. The line absorption and polarization is treated in the context of Unno's (1956) equations and the line broadening theory and method of solution of the equations are presented. The computer programme to combine all aspects of the models is described in some detail, the calculated absorption and polarization spectra are presented and compared with the observations. Good overall agreement was achieved. The successes and failures of the approach are discussed together with suggestions for future work. The current observational and theoretical picture for the ZZ Ceti stars is discussed and the analysis of ZZ Ceti (Robinson et al.,1976) is examined in detail. An extensive programme of high-speed photometry on L 19-2 is reported, and the data reduction techniques described. Initial analysis of the reduced data with the approach of Robinson et al. was found to be fraught with difficulties. Instead, frequency analysis was performed using the technique of power spectra of unequally-spaced data (Deeming,1975). Five oscillation periods were discovered: 350, 192, 143, 113 and 118 seconds. Each of these was found to be amplitude variable. The 192 s oscillation was found to be comprised of a nearly equally spaced triplet of frequency components. Second-order effects in the frequency splitting were discovered. Thus, strong evidence was provided for the presence of rotational splitting of oscillation modes in the low amplitude ZZ Ceti stars. The remaining four oscillation modes were found to have two components each, with a third suspected in two cases. No equal frequency splitting was seen in any of these. No other frequencies with amplitudes exceeding 0.0001 mag were detected in the 100 to 1000 s period range. A proposed mode identification is given and the uncertainties in the theory discussed. L 19-2 was found to have no detectable period variations over the 4.5 year interval spanned by all available observations and was thus found to be another very stable white dwarf pulsator.