  We consider a number of strongly-correlated quantum Hall states which are
likely to be realized in bilayer quantum Hall systems at total Landau level
filling fraction ${\nu_T}=1$. One state, the $(3,3,-1)$ state, can occur as an
instability of a compressible state in the large $d/l_B$ limit, where $d$ and
$l_B$ are the interlayer distance and magnetic length, respectively. This state
has a hierarchical descendent which is interlayer coherent. Another interlayer
coherent state, which is expected in the small $d/l_B$ limit is the well-known
Halperin $(1,1,1)$ state. Using the concept of composite fermion pairing, we
discuss the wavefunctions which describe these states. We construct a phase
diagram using the Chern-Simons Landau-Ginzburg theory and discuss the
transitions between the various phases. We propose that the longitudinal and
Hall drag resistivities can be used together with interlayer tunneling to
experimentally distinguish these different quantum Hall states. Our work
indicates the bilayer ${\nu_T}=1$ quantum Hall phase diagram to be considerably
richer than that assumed so far in the literature.
