  Experimental studies of the transitions from a primary quantum Hall (QH)
liquid at filling factor 1/k (with k an odd integer) to the insulator have
indicated a ``quantized Hall insulator'' (QHI) behavior: while the longitudinal
resistivity diverges with decreasing temperature and current bias, the Hall
resistivity remains quantized at the value $k h/ e^2$. We review the
experimental results and the theoretical studies addressing this phenomenon. In
particular, we discuss a theoretical approach which employs a model of the
insulator as a random network of weakly coupled puddles of QH liquid at fixed
filling factor. This model is proved to exhibit a robust quantization of the
Hall resistivity, provided the electron transport on the network is INCOHERENT.
Subsequent theoretical studies have focused on the controversy whether the
assumption of incoherence is necessary. The emergent conclusion is that in the
quantum coherent transport regime, quantum interference destroys the QHI as a
consequence of localization. Once the localization length becomes much shorter
than the dephasing length, the Hall resistivity diverges. We conclude by
mentioning some recent experimental observations and open questions.
