Neuronal activity in several brain regions is state dependent. This is best exemplified by the dramatic changes that occur in the electroencephalogram as states of vigilance transition from waking to sleep leading to brain waves of various frequencies. The main generator of these state dependent rhythmic activities is the thalamocortical system, a reciprocally interconnected network consisting of thalamocortical relay neurons, two types of thalamic inhibitory neurons including thalamic reticular neurons and local circuit interneurons and various neocortical principal cells and inhibitory interneurons. In the absence of sensory inputs, as happens during sleep and relaxed wakefulness neurons in the thalamus and neocortex engage in stereotyped rhythmic activity patterns spanning a wide range of frequencies, including slow waves, d-waves and sleep spindles. The generation of these rhythms is governed by an interplay between spatially and temporally coordinated synaptic interactions and intrinsic membrane properties of various thalamic and cortical neurons. Thalamic involvement in NREM sleep rhythms relies on a peculiar intrinsic cellular substrate of thalamic burst firing, the low-threshold Ca2+ spike. Cortico-thalamo-cortical synaptic interactions fine tune these intrinsic activity patterns to generate the plethora of state-dependent rhythmic activities.