Grid-connected transformerless photovoltaic (PV) inverters (TPVIs) are increasingly dominating the market due to their higher efficiency, lower cost, lighter weight, and reduced size when compared to their transformer based counterparts. However, due to the lack of galvanic isolation in the low voltage grid interconnections of these inverters, the PV systems become vulnerable to leakage currents flowing through the grounded star point of the distribution transformer, the earth, and the distributed parasitic capacitance of the PV modules. These leakage currents are prohibitive, since they constitute an issue for safety, reliability, protection coordination, electromagnetic compatibility, and module lifetime. This paper investigates a wide range of multi-kW range power rating TPVI topologies and classifies them in terms of their leakage current attributes. This systematic classification places most topologies under a small number of classes with basic leakage current attributes. Thus, understanding and evaluating these topologies becomes an easy task. In addition, based on these observations, new topologies with reduced leakage current characteristics are proposed in this paper. Furthermore, the important efficiency and cost determining characteristics of converters are studied to allow design engineers to include cost and efficiency as deciding factors in selecting a converter topology for PV applications.