Under physiological conditions, slow conduction is essential for the function of the atrioventricular (AV) node, whereas, under pathophysiological conditions, slow conduction contributes importantly to the generation of life-threatening reentrant arrhythmias. This article addresses characteristics of slow conduction at the cellular network level during (a) a reduction of excitability, (b) a reduction of gap junctional coupling, and (c) in the setting of branching tissue structures. Microscopic impulse propagation in these settings was studied by using multiple site optical recording of transmembrane voltage in conjunction with patterned growth cultures of neonatal rat ventricular myocytes. In linear cell strands, a reduction of excitability slowed conduction by approximately 70% before block occurred. In contrast, critical reduction of gap junctional coupling induced a much higher degree of slowing (>99%) before block of conduction. Interestingly, a similar degree of conduction slowing was also observed in branching tissue structures under conditions of reduced excitability (98%). The finding of extremely slow but nevertheless safe conduction in these structures might be explained by a "pull and push" effect of the branches: by drawing electronic current from the activation wavefront, they first act as current loads which slow conduction at the branch points ("pull" effect). Then, on activation, they turn into current sources which feed current back into the system, thus supporting downstream activation and enhancing the safety of propagation ("push" effect). This "pull and push" mechanism may play a significant role in slow conduction in the AV node and in structurally discontinuous myocardium, such as the border regions of infarct scars.