Visuospatial attention produces myriad effects on the activity and selectivity of cortical neurons. Spiking neuron models capable of reproducing a wide variety of these effects remain elusive. We present a model called the Attentional Routing Circuit (ARC) that provides a mechanistic description of selective attentional processing in cortex. The model is described mathematically and implemented at the level of individual spiking neurons, with the computations for performing selective attentional processing being mapped to specific neuron types and laminar circuitry. The model is used to simulate three studies of attention in macaque, and is shown to quantitatively match several observed forms of attentional modulation. Specifically, ARC demonstrates that with shifts of spatial attention, neurons may exhibit shifting and shrinking of receptive fields; increases in responses without changes in selectivity for non-spatial features (i.e. response gain), and; that the effect on contrast-response functions is better explained as a response-gain effect than as contrast-gain. Unlike past models, ARC embodies a single mechanism that unifies the above forms of attentional modulation, is consistent with a wide array of available data, and makes several specific and quantifiable predictions.