Mouse models of rare monogenic forms of migraine provide a unique experimental system to study the cellular and circuit mechanisms of the primary brain dysfunctions causing a migraine disorder. Here, we discuss the migraine-relevant phenotypes and the migraine-relevant functional alterations in the brain of five genetic mouse models of migraine, four of which carry mutations derived from patients with familial hemiplegic migraine (FHM) and the fifth carry a mutation from patients with both phenotypically normal MA and familial advanced sleep phase syndrome (FASPS). We focus on the latter mouse model, in which a ubiquitous serine-threonine kinase is mutated, and on two mouse models of pure FHM, in which a voltage-gated calcium channel controlling neurotransmitter release at most brain synapses and a Na/K ATPase that is expressed mainly in astrocytes in the adult brain are mutated, respectively. First, we describe the behavioral phenotypes of the genetic animal models and review the evidence that an increased susceptibility to experimentally induced cortical spreading depression (CSD) is a key migraine-relevant phenotype common to the five models. Second, we review the synaptic alterations in the cerebral cortex of the genetic models of migraine and discuss the mechanisms underlying their increased susceptibility to CSD. Third, we review the alterations in the trigeminovascular pain pathway and discuss possible implications for migraine pain mechanisms. Finally, we discuss the insights into migraine pathophysiology obtained from the genetic models of migraine, in particular regarding the mechanisms that make the brain of migraineurs susceptible to the ignition of "spontaneous" CSDs. Although the reviewed functional studies support the view of migraine as a disorder of the brain characterized by dysfunctional regulation of the excitatory/inhibitory balance in specific neuronal circuits, much work remains to be done in the genetic mouse models e.g. to identfy the relevant dysfunctional circuits and to establish whether and how the alterations in the function of specific circuits (in the cerebral cortex and/or other brain areas) are state-dependent and may, in certain conditions, favor CSD ignition and the migraine attack.