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The inevitable choice for the automotive industry to suppress greenhouse gas emissions is zero-emission vehicles such as battery electric vehicles. Some of the main barriers regarding the adoption of electric vehicles are range anxiety, and lack of charging infrastructure, which can be addressed by ultra-fast chargers or charging stations. The conventional ultra-fast chargers are low-voltage (LV) connected through line-frequency transformers, which pose disadvantages such as low efficiency, high cost, and large footprints. The medium-voltage (MV) connected charging station is proposed by the researchers to overcome the challenges regarding the conventional chargers by eliminating the line-frequency transformer and direct connection to the medium voltage. The most challenging part of the medium-voltage ultra-fast chargers is the AC/DC stage connection to the medium voltage. Different medium-voltage multilevel converters have been proposed to facilitate the direct connection to the medium-voltage grid. However, disadvantages such as a high number of components and control complexity weaken the strength of medium-voltage connected stations. The main focus of this thesis is on novel advanced medium-voltage multilevel topologies and control techniques for medium-voltage connected ultra-fast EV charging applications. First, a novel controller based on SPWM is proposed to control the flying capacitor voltages of a four-level T-type Nested Neutral Point Clamped (NNPC) topology. Second, a new five-level T-type NNPC topology is proposed that has a minimum number of components in comparison to other existing five-level topologies. To extend the voltage and power rating, a novel seven-level topology is proposed that has the lowest number of components in comparison to other existing topologies. Moreover, three different controllers are developed to control the voltages of the seven-level topology based on Model Predictive Control, where the challenges regarding significant computational burden and weighting factor elimination are addressed. Finally, an MV-connected ultra-fast charging station architecture is proposed, where the proposed seven-level topology is considered as the AC/DC stage. Comparison of the proposed topology to the LV-connected stations shows that the efficiency, cost, and power quality of the charging stations can be improved significantly. Thesis Doctor of Philosophy (PhD)