Scrutiny of the numerous physiology and imaging studies of visual attention reveal that integration of results from neuroscience with the classic theories of visual attention based on behavioral work is not simple. The different subfields have pursued different questions, used distinct experimental paradigms and developed diverse models. The purpose of this review is to use statistical decision theory and computational modeling to relate classic theories of attention in psychological research to neural observables such as mean firing rate or functional imaging BOLD response, tuning functions, Fano factor, neuronal index of detectability and area under the receiver operating characteristic (ROC). We focus on cueing experiments and attempt to distinguish two major leading theories in the study of attention: limited resources model/increased sensitivity vs. selection/differential weighting. We use Bayesian ideal observer (BIO) modeling, in which predictive cues or prior knowledge change the differential weighting (prior) of sensory information to generate predictions of behavioral and neural observables based on Gaussian response variables and Poisson process neural based models. The ideal observer model can be modified to represent a number of classic psychological theories of visual attention by including hypothesized human attentional limited resources in the same way sequential ideal observer analysis has been used to include physiological processing components of human spatial vision (Geisler, W. S. (1989). Sequential ideal-observer analysis of visual discrimination. Psychological Review 96, 267–314.). In particular we compare new biologically plausible implementations of the BIO and variant models with limited resources. We find a close relationship between the behavioral effects of cues predicted by the models developed in the field of human psychophysics and their neuron-based analogs. Critically, we show that cue effects on experimental observables such as mean neural activity, variance, Fano factor and neuronal index of detectability can be consistent with the two major theoretical models of attention depending on whether the neuron is assumed to be computing likelihoods, log-likelihoods or a simple model operating directly on the Poisson variable. Change in neuronal tuning functions can also be consistent with both theories depending on whether the change in tuning is along the dimension being experimentally cued or a different dimension. We show that a neuron's sensitivity appropriately measured using the area under the Receive Operating Characteristic curve can be used to distinguish across both theories and is robust to the many transformations of the decision variable. We provide a summary table with the hope that it might provide some guidance in interpreting past results as well as planning future studies.