One of the possible SOFC system-configurations providing the highest potential of electrical DC-efficiency of up to 65% is a SOFC-system with anode exhaust gas recirculation (AEGR), where part of the depleted anode exhaust gas is recirculated and mixed with fresh natural gas upstream of the reformer. For safe and durable operation of a SOFC-system, the oxygen-to-carbon-ratio and the fuel utilization as characteristic parameters must not exceed stack- and reformer-specific thresholds. The determination and control of the characteristic parameters are therefore of crucial importance. However, this poses especially for SOFC-systems with AEGR due to enhanced system complexity a challenging task. In this paper, the authors present an overview on representative control strategies as well as different approaches to determine or diagnose characteristic parameters with emphasis on SOFC-systems with AEGR. Some conclusions are discussed based on the provided overview and outlines recommendations for future research work.