Cortical neurons continuously transform sets of incoming spike trains into output spike trains. This input-output transformation is referred to as single-neuron computation and constitutes one of the most fundamental process in the brain. A deep understanding of single-neuron dynamics is therefore required to study how neural circuits support complex behaviors such as sensory perception, learning and memory. The results presented in this thesis focus on single-neuron computation. In particular, I address the question of how and why cortical neurons adapt their coding strategies to the statistical properties of their inputs. A new spiking model and a new fitting procedure are introduced that enable reliable nonparametric feature extraction from in vitro intracellular recordings. By applying this method to a new set of data from L5 pyramidal neurons, I found that cortical neurons adapt their firing rate over multiple timescales, ranging from tens of milliseconds to tens of second. This behavior results from two cellular processes, which are triggered by the emission of individual action potentials and decay according to a power-law. An analysis performed on in vivo intracellular recordings further indicates that power-law adaptation is near-optimally tuned to efficiently encode natural inputs received by single neurons in biologically relevant situations. These results shade light on the functional role of spike-frequency adaptation in the cortex. The second part of this thesis focuses on the long-standing question of whether cortical neurons act as temporal integrators or coincidence detectors. According to standard theories relying on simplified spiking models, cortical neurons are expected to feature both coding strategies, depending on the statistical properties of their inputs. A model-based analysis performed on a second set of in vitro recordings demonstrates that the spike initiation dynamics implements a complex form of adaptation to make cortical neurons act as coincidence detectors, regardless of the input statistics. This result indicates that cortical neurons are well-suited to support a temporal code in which the relevant information is carried by the precise timing of spikes. The spiking model introduced in this thesis was not designed to study a particular aspect of single-neuron computation and achieves good performances in predicting the spiking activity of different neuronal types. The proposed method for parameter estimation is efficient and only requires a limited amount of data. If applied on large datasets, the mathematical framework presented in this thesis could therefore lead to automated high-throughput single-neuron characterization.