Lower-limb amputation results in mobility impairments that adversely affect activities of daily living, such as walking on uphill and downhill slopes. Sloped walking is characterized by greater muscular demands and higher risk of slipping compared to level-ground walking, and is more difficult for people with transtibial amputation relative to able-bodied people. The greater difficulty of sloped walking for this population is due at least in part to the lost function of the ankle plantarflexor muscles, which are critical for propelling the body forward and maintaining dynamic balance. Passive prostheses are typically prescribed following amputation, but these devices do not replace the net positive mechanical power generation of the plantarflexors. Alternatively, powered prostheses generate mechanical power using a motorized ankle joint and have been shown to better replicate normative ankle mechanics and reduce the metabolic cost of level-ground walking relative to passive prostheses. However, how the use of powered prostheses affects balance and muscle function in comparison to passive prostheses during sloped walking remains unclear. In addition, while powered prostheses are tuned to provide normative ankle torque and power during walking, they may still result in altered biomechanics at other joints relative to able-bodied people because of compromised function of the biarticular gastrocnemius, an ankle plantarflexor muscle that spans both the knee and ankle. Therefore, the overall purpose of this work was to provide a quantitative analysis of the biomechanical function of powered and passive prostheses as well as their effects on dynamic balance during sloped walking. A variety of methods were used to assess dynamic balance, including whole-body angular momentum, margin of stability, foot placement estimate and capture point. Musculoskeletal modeling and simulation were also used to quantify prosthesis and muscle function during sloped walking. The contributions of the prostheses and individual muscles to mechanical power in the trunk and legs were used to assess the effects of different types of prostheses on muscle compensations and coordination of movement. The results provide an evaluation of the performance of powered and passive prostheses during sloped walking and identify goals for future prosthesis design.