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Intracellular electrophysiological recordings provide crucial insights into elementary neuronal signals such as action potentials and synaptic currents. Analyzing and interpreting these signals is essential for a quantitative understanding of neuronal information processing, and requires both fast data visualization and ready access to complex analysis routines. To achieve this goal, we have developed Stimfit, a free software package for cellular neurophysiology with a Python scripting interface and a built-in Python shell. The program supports most standard file formats for cellular neurophysiology and other biomedical signals through the Biosig library. To quantify and interpret the activity of single neurons and communication between neurons, the program includes algorithms to characterize the kinetics of presynaptic action potentials and postsynaptic currents, estimate latencies between pre- and postsynaptic events, and detect spontaneously occurring events. We validate and benchmark these algorithms, give estimation errors, and provide sample use cases, showing that Stimfit represents an efficient, accessible and extensible way to accurately analyze and interpret neuronal signals.