Recent advances in the application of nontraditional methods and procedures for offline diagnosis and online monitoring of new and service-aged power transformers are discussed. Advanced offline methods are based on the main operational stresses (electrical, mechanical, thermal) and on typical failure modes: measurement of polarisation and depolarisation currents, electrical detection of partial discharges and measurement of the transfer function. A pilot installation of an online monitoring system on a strategically important transformer is described. The measured data of the built-in sensors (e.g. load, temperatures, gas and moisture in oil, overvoltages) are analyzed using a model-based software approach with an adaptive threshold to define faulty conditions