  Fractional quantum Hall states at half-integer filling factors have been
observed in many systems beyond the $5/2$ and $7/2$ plateaus in GaAs quantum
wells. This includes bilayer states in GaAs, several half-integer plateaus in
ZnO-based heterostructures, and quantum Hall liquids in graphene. In all cases,
Cooper pairing of composite fermions is believed to explain the plateaus. The
nature of Cooper pairing and the topological order on those plateaus are hotly
debated. Different orders are believed to be present in different systems. This
makes it important to understand experimental signatures of all proposed
orders. We review the expected experimental signatures for all possible
composite-fermion states at half-integer filling. We address Mach-Zehnder
interferometry, thermal transport, tunneling experiments, and Fabry-P\'{e}rot
interferometry. For this end, we introduce a uniform description of the
topological orders of Kitaev's sixteenfold way in terms of their
wave-functions, effective Hamiltonians, and edge theories.
