Fast progress in near-net-shape production of parts has attracted vast interest in internal surface finishing. Interest in designing a modern finishing machine to cover the different shapes of workpieces with different materials has risen recently, and the current state of technology cannot satisfy the high requirements for finishing internal channels in metal-additive-manufactured parts. Therefore, in this work, an effort has been made to close the current gaps. This literature review aims to trace the development of different non-traditional internal surface finishing methods. For this reason, attention is focused on the working principles, capabilities, and limitations of the most applicable processes, such as internal magnetic abrasive finishing, abrasive flow machining, fluidized bed machining, cavitation abrasive finishing, and electrochemical machining. Thereafter, a comparison is presented based on which models were surveyed in detail, with particular attention to their specifications and methods. The assessment is measured by seven key features, with two selected methods deciding their value for a proper hybrid machine.