After a brief introduction, we study the constraints on MSSM the Higgs
sector parameters from the non-observation of any Higgs boson signals
in experiments at LEP. We also review the range of Higgs boson masses
that can be searched for at LEP 200. For the most part, we focus on t
he prospects for the detection of MSSM Higgs bosons in experiments at
hadron supercolliders, assuming that these are too heavy to be discove
red at LEP 200. We then show that supersymmetric decays of Higgs boson
s can significantly reduce the rates for event topologies usually used
for Higgs searches. Finally, we discuss some promising new channels f
or MSSM Higgs boson detection that become possible if these SUSY decay
s are allowed.