  Since the discovery of the first L dwarf 19 years ago and the discovery of
the first T dwarf 7 years after that, we have amassed a large list of these
objects, now numbering almost six hundred. Despite making headway in
understanding the physical chemistry of their atmospheres, some important
issues remain unexplained. Three of these are the subject of this paper: (1)
What is the role of "second parameters" such as gravity and metallicity in
shaping the emergent spectra of L and T dwarfs? Can we establish a robust
classification scheme so that objects with unusual values of log(g) or [M/H],
unusual dust content, or unresolved binarity are easily recognized? (2) Which
physical processes drive the unusual behavior at the L/T transition? Which
observations can be obtained to better confine the problem? (3) What will
objects cooler than T8 look like? How will we know a Y dwarf when we first
observe one?
