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Fractional quantum Hall states at half-integer filling factors have beenobserved in many systems beyond the $5/2$ and $7/2$ plateaus in GaAs quantumwells. This includes bilayer states in GaAs, several half-integer plateaus inZnO-based heterostructures, and quantum Hall liquids in graphene. In all cases,Cooper pairing of composite fermions is believed to explain the plateaus. Thenature of Cooper pairing and the topological order on those plateaus are hotlydebated. Different orders are believed to be present in different systems. Thismakes it important to understand experimental signatures of all proposedorders. We review the expected experimental signatures for all possiblecomposite-fermion states at half-integer filling. We address Mach-Zehnderinterferometry, thermal transport, tunneling experiments, and Fabry-P\'{e}rotinterferometry. For this end, we introduce a uniform description of thetopological orders of Kitaev's sixteenfold way in terms of theirwave-functions, effective Hamiltonians, and edge theories.

The sixteenfold way and the quantum Hall effect at half-integer filling factors