Microfluidic impedance cytometry is a label-free technique for high-throughput single-cell analysis. Multi-frequency impedance measurements provide data that allows full characterisation of cells, linking electrical phenotype to individual biophysical properties. To efficiently extract the information embedded in the electrical signals, potentially in real-time, tailored signal processing is needed. Artificial intelligence approaches provide a promising new direction. Here we demonstrate the ability of neural networks to decipher impedance cytometry signals in two challenging scenarios: (i) to determine the intrinsic dielectric properties of single cells directly from raw impedance data streams, (ii) to capture single-cell signals that are hidden in the measured signals of coincident cells. The accuracy of the results and the high processing speed (fractions of ms per cell) demonstrate that neural networks can have an important role in impedance-based single-cell analysis.