Although many progresses have been made on the topic since the classical work of Frenkel,
the Poole-Frenkel formula has been spreadly used to interpret several non-ohmic experimental currents observed in dielectrics and also semiconductors. 
The debate about the underlying assumptions of the classical Poole-Frenkel model has given life to several improved Poole-Frenkel models. 
These hypotheses are presented in the following.
Only electron (single-carrier) conduction is considered, assuming the existence of ohmic contacts capable to refill detrapped electrons at the electrodes, and space charge effects are neglected, supposing that the field is uniform. A revisitation of this latter assumption can be found, for example, in the “theory of space charge limited current enhanced by Frenkel effect” developed by Murgatroyd.
The carriers mobility is assumed to be field-independent. Neglecting every kind of diffusion process for the de-trapped carriers, the pre-exponential factor in the Poole-Frenkel formula is thus proportional to . This depiction would be suitable for the description of the conduction either in dielectrics or semiconductors. However, Poole–Frenkel effect is likely to be observed only in materials characterized by low mobility values, for, in high mobility solids, the re-trapping of carriers would be gradually inhibited by carrier depletion.
Still, different dependences of the pre-exponential factor from the field can be found: assuming that the carriers could be re-trapped, proportionality to  or  is obtained, depending on the electron retrapping occurring by the nearest neighbouring trap or after a drift. Moreover, a pre-exponential factor proportional to  is found to be the result of random diffusion processes, while dependencies on  and  are found to be the result of hopping and diffusion transport processes respectively.
In the classical Poole-Frenkel theory a Coulombic trap potential is assumed, but steeper potentials belonging to multipolar defects or screened hydrogenic potentials are considered as well.
Regarding the typology of traps, the Poole–Frenkel effect is described to occur for positively charged trap sites, i.e. for traps that are positive when empty and neutral when filled, in order for the electron to experience a Coulombic potential barrier due to the interaction with the positively charged trap. Donors or acceptors sites and electrons in the valence band will also exhibit the Poole–Frenkel effect as well. On the contrary, a neutral trap site, i.e. a site that is neutral when empty and charged (negatively for electrons) when filled, will not exhibit Poole–Frenkel effect.
Among the others, Simmons has proposed an alternative to the classical model with shallow neutral traps and deep donors, capable to exhibit a bulk-limited conduction with a Schottky electric field dependence, even in presence of a Poole-Frenkel conduction mechanism, thus explaining the "anomalous Poole-Frenkel effect" revealed by TaO and SiO films.
Models there exist that consider the presence of both donor and acceptor trap sites, in a situation called compensation of traps.
The model of Yeargan and Taylor, for example, extends the classical Poole-Frenkel theory including diverse degrees of compensations: when only one kind of trap is considered, the slope of the curve in a Poole-Frenkel plot reproduces that obtained from Schottky emission, in spite of the barrier lowering being twice that for Schottky effect; the slope is twice larger in presence of compensation.
As a further assumption a single energy level for the traps is assumed. However, the existence of further donor levels is discussed, even if they are supposed to be entirely filled for every field and temperature regime, and thus to not furnish any conduction carrier (this is equivalent to state that the additional donor levels are placed well below the Fermi level).