  Plasma wakefield acceleration (PWFA) is a promising method for reducing the
scale and cost of future electron-positron collider experiments by using
shorter plasma sections to enhance beam energy. While electron acceleration has
already achieved breakthroughs in theory and experimentation, generating
high-quality positron beams in plasma presents greater challenges, such as
controlling emittance and energy spread, improving energy conversion
efficiency, and generating positron sources. In this paper, we have summarized
the research progress on advanced positron acceleration schemes, including
particle beam-driven wakefield acceleration, laser-driven wakefield
acceleration, radiation-based acceleration, hollow plasma channels, among
others. The strengths and weaknesses of these approaches are analyzed, and the
future outlook is discussed to drive experimental advancements.
