  According to standard evolutionary theory for cataclysmic variables (CVs),
angular momentum loss drives CVs to initially evolve from longer to shorter
orbital periods until a minimum period is reached (\approx 80 min). At roughly
this stage, the donors becomes degenerate, expand in size, and the systems move
towards longer Porb. Theory predicts that 70% of all CVs should have passed
their minimum period and have sub-stellar donors, but until recently, no such
systems were known. I present one CV showing evidence of harbouring a sub-dwarf
donor, SDSS J1507+52. Due to the system's unusually short Porb of about 65 min,
and very high space velocity, two origins for SDSS J1507+52 have been proposed;
either the system was formed from a young WD/brown-dwarf binary, or the system
is a halo CV. In order to distinguish between these two theories, I present UV
spectroscopy and find a metallicity consistent with halo origin. Systems close
to Pmin are expected to have low accretion rates. Some of these CVs show
absorption in their spectra, implying that the underlying WD is exposed. This
yields a rare opportunity to study the WD in a CV. I introduce two new systems
showing WD signatures in their light curves and spectra, SDSS J1457+51 and BW
Scl. Despite the fact that CVs close to Pmin should be faint, we find systems
that are much too bright for their Porb. Such a system is T Pyx - a recurrent
nova with an unusually high accretion rate and a photometrically determined
Porb < 2 hr. T Pyx is about 2 times brighter than any other CV at its period.
However, to confirm its evolutionary status, a more reliable period
determination is needed. Here, I present a spectroscopic study, confirming T
Pyx as a short-period CV. In this thesis, I discuss what implications these
systems may have on the current understanding of CV evolution, and the
importance of studying individual systems in general.
