Calcium dynamics in presynaptic terminals regulate the response dynamics of most central excitatory synapses. However, this dogma has been challenged by the hypothesis that mobility of the postsynaptic alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid subtype glutamate receptors (AMPAR) plays a role in tuning fast excitatory synaptic transmission. In this review, we reevaluate the factors regulating postsynaptic AMPAR mobility, reassess the modeling parameters, analyze the experimental tools, and end by providing alternative ideas stemming from recent results. In particular, newer methods of labeling AMPARs with small fluorophores in live neurons, combined with super-resolution microscopy and sub-second dynamics, lends support to the idea that AMPARs are primarily within the synapse, are greatly constrained, and have much slower mobility than previously thought. We discuss new experiments which may be necessary to readdress the role of postsynaptic AMPAR mobility in tuning fast excitatory synaptic transmission.