Inductorless switch mode power supplies based on piezoelectric transformers are used to replace conventional transformers in high power density switch mode power supplies. Even though piezoelectric-based converters exhibit a high degree of nonlinearity, it is desirable to use piezoelectric transformers due to their smaller size, lighter weight, lower electromagnetic interference, higher power density, higher efficiency, and lower cost. Moreover, PTs allow converters to operate in high switching frequencies and by obtaining soft switching condition, switching losses will decrease. This paper discusses power supplies with the trend evaluation of piezoelectric transformer-based converter topologies and control methods. The challenges of piezoelectric transformers regarding soft switching capability and nonlinearity are addressed. This paper can be used as a guideline for choosing a proper topology of piezoelectric-based switch mode power supply and a control method for the required application.