Solid oxide fuel cells (SOFCs) are high temperature electrochemical devices with the potential for clean and efficient power generation. The electrodes, which support the electrochemical reactions, play a vital role in determining the performance and durability of these devices. Effective electrode materials must balance a spectrum of criteria, including cost, thermal and chemical stability, electronic conductivity and catalytic activity. A number of successful electrode materials have been identified; the most widely adopted materials are composite structures providing electronic, ionic and gas phase percolation, which promotes electrochemical activity throughout the bulk of the electrode. The contiguous contact of electronic, ionic and gas phases at so called triple phase boundaries provides a direct indication of the electrochemical activity of the electrode. Improvements in tomography techniques have allowed SOFC electrode microstructures to be characterised in three dimensions, giving unprecedented access to a wealth of microstructural information on the nature of triple phase contact and percolation. With improved availability of advanced tomographic techniques, fuel cell developers are increasingly equipped to link processing routes to electrode microstructure and in turn electrochemical performance, such that the intelligent engineering of SOFC electrodes is becoming a reality. Here we review the development and application of these advanced microstructural characterisation techniques.