Synchronous neuronal activity in the thalamocortical system is critical for a number of behaviorally relevant computations, but hypersynchrony can limit information coding and lead to epileptiform responses. In the somatosensory thalamus, afferent inputs are transformed by networks of reciprocally connected thalamocortical neurons in the ventrobasal nucleus (VB) and GABAergic neurons in the thalamic reticular nucleus (TRN). These networks can generate oscillatory activity, and studies in vivo and in vitro have suggested that thalamic oscillations are often accompanied by synchronous neuronal activity, in part mediated by widespread divergence and convergence of both reticulothalamic and thalamoreticular pathways, as well as by electrical synapses interconnecting TRN neurons. However, the functional organization of thalamic circuits and its role in shaping input-evoked activity patterns remain poorly understood. Here we show that optogenetic activation of cholinergic synaptic afferents evokes near-synchronous firing in mouse TRN neurons that is rapidly desynchronized in thalamic networks. We identify several mechanisms responsible for desynchronization: (1) shared inhibitory inputs in local VB neurons leading to asynchronous and imprecise rebound bursting; (2) TRN-mediated lateral inhibition that further desynchronizes firing in the VB; and (3) powerful yet sparse thalamoreticular connectivity that mediates re-excitation of the TRN but preserves asynchronous firing. Our findings reveal how distinct local circuit features interact to desynchronize thalamic network activity.