ABSTRACT: The output of neocortical layer 5 pyramidal cells (L5PCs) is expressed by a train of single spikes with intermittent bursts of multiple spikes at high frequencies. The bursts are the result of nonlinear dendritic properties, including Na+, Ca2+, and NMDA spikes, that interact with the ~10,000 synapses impinging on the neuron’s dendrites. Output spike bursts are thought to implement key dendritic computations, such as coincidence detection of bottom-up inputs (arriving mostly at the basal tree) and top-down inputs (arriving mostly at the apical tree). In this study we used a detailed nonlinear model of L5PC receiving excitatory and inhibitory synaptic inputs to explore the conditions for generating bursts and for modulating their properties. We established the excitatory input conditions on the basal versus the apical tree that favor burst and show that there are two distinct types of bursts. Bursts consisting of 3 or more spikes firing at < 200 Hz, which are generated by stronger excitatory input to the basal versus the apical tree, and bursts of ~2-spikes at ~250 Hz, generated by prominent apical tuft excitation. Localized and well-timed dendritic inhibition on the apical tree differentially modulates Na+, Ca2+, and NMDA spikes and, consequently, finely controls the burst output. Finally, we explored the implications of different burst classes and respective dendritic inhibition for regulating synaptic plasticity. Author summary The output of most neurons consists of stereotypical electrical pulses, or spikes. Some neurons generate sparse spikes intertwined with groups of spikes in close succession, called bursts. Previous research has implicated bursts in long-range transmission, dendritic computation, and plasticity. However, a detailed account of the spatiotemporal synaptic activation patterns that generate bursts, even in the principal cortical pyramidal neurons, is largely missing. Using experimentally constrained computational modelling we determined the conditions of synaptic activation patterns that induce burst firing in these cells. We found two distinct classes of bursts. They are distinguished by the number of active synapses, on either basal or apical part of the dendritic tree, required for burst initiation, and by the number and frequency of output spikes. We provide an analysis of how location and timing of dendritic inhibition finely edit somatic bursts and show the change in the strength of excitatory synapses during bursts following their dendritic inhibition. Overall, this work offers a deeper understanding of the origin of bursts, including a novel distinction between burst classes and characterization of how inhibition may shape bursts and their correlated synaptic plasticity.