  Understanding the nature of the luminous 1991T-like supernovae is of great
importance to supernova cosmology as they are likely to have been more common
in the early universe. In this paper we explore the observational properties of
1991T-like supernovae to study their relationship to other luminous,
slow-declining Type~Ia supernovae (SNe Ia). From the spectroscopic and
photometric criteria defined in Phillips et al. (1992), we identify 17
1991T-like supernovae from the literature. Combining these objects with ten
1991T-like supernovae from the Carnegie Supernova Project-II, the spectra,
light curves, and colors of these events, along with their host galaxy
properties, are examined in detail. We conclude that 1991T-like supernovae are
closely related in essentially all of their UV, optical, and near-infrared
properties -- as well as their host galaxy parameters -- to the slow-declining
subset of Branch core-normal supernovae and to the intermediate 1999aa-like
events, forming a continuum of luminous SNe Ia. The overriding difference
between these three subgroups appears to be the extent to which $^{56}$Ni mixes
into the ejecta, producing the pre-maximum spectra dominated by Fe III
absorption, the broader UV light curves, and the higher luminosities that
characterize the 1991T-like events. Nevertheless, the association of 1991T-like
SNe with the rare Type Ia CSM supernovae would seem to run counter to this
hypothesis, in which case 1991T-like events may form a separate subclass of SNe
Ia, possibly arising from single-degenerate progenitor systems.
