Electrical impedance tomography (EIT) is a medical imaging technique based on the injection of a current or voltage pattern through electrodes on the skin of the patient, and on the reconstruction of the internal conductivity distribution from the voltages collected by the electrodes. Compared to other imaging techniques, EIT shows significant advantages: it does not use ionizing radiation, is non-invasive and is characterized by high temporal resolution. Moreover, its low cost and high portability make it suitable for real-time, bedside monitoring. However, EIT is also characterized by some technical limitations that cause poor spatial resolution. The possibility to design wearable devices based on EIT has recently given a boost to this technology. In this paper we reviewed EIT physical principles, hardware design and major clinical applications, from the classical to a wearable setup. A wireless and wearable EIT system seems a promising frontier of this technology, as it can both facilitate making clinical measurements and open novel scenarios to EIT systems, such as home monitoring.