Wide band-gap semiconductor materials such as silicon carbide (SiC) and gallium nitride (GaN) have been widely investigated these years for their preferred operation at higher switching frequency, higher blocking voltage, higher temperature, with a compacter volume, in comparison with the traditional silicon (Si) devices. SiC MOSFETs have been utilized in photovoltaic systems, wind turbine converters, electric vehicles, solid-state transformers, more electric ships, and airplanes. GaN based transistors have also been adopted in the DC-to-DC converters in data centers, personal computers, AC-to-DC power factor correction converters for the consumer electronic adaptors, and DC-to-AC photovoltaic micro-inverters. The first part of this dissertation is regarding the lifetime modeling and condition monitoring for the SiC MOSFETs. Since SiC-based devices have different failure modes and mechanisms compared with Si counterparts, a comprehensive review will be conducted to develop accurate lifetime prediction, condition monitoring, and lifetime extension strategies. First, a novel comprehensive online updated system-level lifetime modeling approach will be presented. Second, to monitor the SiC MOSFET ageing, the typical degradation indicators of SiC MOSFET gate oxide will be investigated. Third, to measure the junction temperature, the dynamic temperature-sensitive electrical parameters for the medium-voltage SiC devices will be studied. The other part is the topology investigation of these emerging wide band-gap devices. A generalized topology that would leverage the advantages of the wide band-gap devices will be introduced and analyzed in detail. Following it is a new evaluation index for comparing different topologies with the consideration of the semiconductor die information. The topology and its derivatives will be utilized in the subsequent chapters for three applications. First, a 100 kW switched tank converter (STC) will be designed using SiC MOSFETs for transportation power electronic systems. Second, an updated STC topology integrating with the partial-power voltage regulation will be introduced for electric vehicle applications. Third, two novel single-phase resonant multilevel modular boost inverters will be designed based on the voltage-regulated STC. These topologies will be validated through designed prototypes. As a result, the high power density and high efficiency will be realized by combining the well-suited topologies and the advantages of the WBG devices.