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Transformerless grid-connected inverters (TLI) feature high efficiency, low cost, low volume, and weight due to using neither line-frequency transformers nor high-frequency transformers. Therefore, TLIs have been extensively investigated in the academic community and popularly installed in distributed photovoltaic grid-connected systems during the past decade. This article analyzes and summarizes the state of the art of TLI techniques, three rules of maintaining constant common-mode voltage (CMV) of TLIs at switching frequency have been concluded from a generic CMV analysis model at the beginning. Second, suppression methods of leakage current (LC) and dc current injection (DCCI), so-called two key challenges for first-generation TLIs, have been classified and discussed in detail, respectively. Finally, future trends and some challenges of TLIs based on wide bandgap devices named second-generation TLIs have been presented in this article. [ABSTRACT FROM AUTHOR]