Current theories and models of brain rhythm generation are based on (1) the excitability of individual neurons and whole networks, (2) the structural and functional connectivity of neuronal ensembles, (3) the dynamic interaction of excitatory and inhibitory network components, and (4) the importance of transient local and global states. From the interplay of the above, systemic network properties arise which account for activity overdrive or suppression, and critical-level synchronization. Under certain conditions or states, small-to-large scale neuronal networks can be entrained into excessive and/or hypersynchronous electrical brain activity (epileptogenesis). In this chapter we demonstrate with artificial neuronal network simulations how physiological brain oscillations (delta, theta, alpha, beta and gamma range, and transients thereof, including sleep spindles and larger sleep waves) are generated and how epileptiform phenomena can potentially emerge, as observed at a macroscopic scale on scalp and intracranial EEG recordings or manifested with focal and generalized, aware and unaware, motor and nonmotor or absence seizures in man. Fast oscillations, ripples and sharp waves, spike and slow wave discharges, sharp and rhythmical slow waves, paroxysmal depolarization and DC shifts or attenuation and electrodecremental responses seem to underlie key mechanisms of epileptogenesis across different scales of neural organization and bear clinical implications for the pharmacological and surgical treatment of the various types of epilepsy.