  Objects in the Kuiper belt are small and far away thus difficult to study in
detail even with the best telescopes available at earth. For much of the early
history of the Kuiper belt, studies of the compositions of these objects were
relegated to collections of moderate quality spectral and photometric data that
remained difficult to interpret. Much early effort was put into simple
correlations of surface colors and identifications of spectral features, but it
was difficult to connect the observations to a larger understanding of the
region. The last decade, however, has seen a blossoming in our understanding of
the compositions of objects in the Kuiper belt. This blossoming is a product of
the discoveries of larger -- and thus easier to study -- objects, continued
dedication to the collection of a now quite large collection of high quality
photometric and spectroscopic observations, and continued work at the
laboratory and theoretical level. Today we now know of many processes which
affect the surface compositions of objects in the Kuiper belt, including
atmospheric loss, differentiation and cryovolcanism, radiation processing, the
effects of giant impacts, and the early dynamical excitation of the Kuiper
belt. We review the large quantity of data now available and attempt to build a
comprehensive framework for understanding the surface compositions and their
causes. In contrast to surface compositions, the bulk compositions of objects
in the Kuiper belt remain poorly measured and even more poorly understood, but
prospects for a deeper understanding of the formation of the the outer solar
are even greater from this subject.
