A solid oxide fuel cell (SOFC) is a promising energy conversion device with high efficiency and low pollutant emission. The practical application of the conventional SOFCs is limited mainly because of their high operating temperature and the inconvenience brought by the H-2 fuel utilization. This work reviews the recent progress on intermediate temperature SOFCs especially with non-hydrogen fuels. Composite electrolyte consisting of a solid oxide ionic conducting phase and a molten carbonate phase exhibits sufficient ionic conductivity in the intermediate temperature range, i.e. 500-800 degrees C, and facilitates the simultaneous conduction of H+, O2- and CO32- ions. A single cell with the composite electrolyte shows a promising power density, 1700 mW cm(-2) at 650 degrees C with hydrogen as the fuel. The composite electrolyte has been also employed in a direct carbon fuel cell (DCFC), and the simultaneous conduction of O2- and CO32- in the electrolyte has been proposed. Recently, perovskite structured materials are found to have good resistance to coke formation as the anode of the direct hydrocarbon solid oxide fuel cell, and several carbon resistant perovskite anodes are employed in all-perovskite structured SOFCs, which exhibit excellent performance with CH4 and methanol as the fuel. Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.