The combination of transcranial magnetic stimulation (TMS) with simultaneous electroencephalography (EEG) provides us the possibility to non-invasively probe the brain's excitability, time-resolved connectivity and instantaneous state. Early attempts to combine TMS and EEG suffered from the huge electromagnetic artifacts seen in EEG as a result of the electric field induced by the stimulus pulses. To deal with this problem, TMS-compatible EEG systems have been developed. However, even with amplifiers that are either immune to or recover quickly from the pulse, great challenges remain. Artifacts may arise from the movement of electrodes, from muscles activated by the pulse, from eye movements, from electrode polarization, or from brain responses evoked by the coil click. With careful precautions, many of these problems can be avoided. The remaining artifacts can be usually reduced by filtering, but control experiments are often needed to make sure that the measured signals actually originate in the brain. Several studies have shown the power of TMS-EEG by giving us valuable information about the excitability or connectivity of the brain.