This paper provides a systematic survey on the topology morphing control techniques used in the galvanically isolated dc-dc converters. Existing techniques are broadly categorized based on the part where a converter changes its topology: at the input side, at the output side, and the advanced techniques that cannot be categorized in the first two groups. The techniques span from the simple reconfiguration between the full-and half-bridge switching cells similar to the conventional power supplies with universal ac input to the advanced multi-track topology and reconfigurable resonant tanks. In addition, the described variety of application examples proves the wide application range and versatility of the topology morphing control. These include fault tolerance, efficiency curve flattening, input voltage range extension, and other properties. Hence, this article provides a single comprehensive source for researchers and engineers willing to enter the topic of topology morphing control.INDEX TERMS Galvanically isolated DC-DC power converter, topology morphing control, series resonant converters.