The combination of advantages in positron acceleration over
plasma-based accelerators and high gradient over conventional
accelerators puts the structure-based wakefield accelerator (SWFA)
in a unique spot on the road to a multi-TeV linear collider. As a
result of the significant advancements that have been made
throughout the past several decades, the SWFA related research
continues gaining special attention from the accelerator
community. In this article, we will present a survey of the research
on SWFAs, with a particular focus on the challenges in beam
dynamics, and lay out a roadmap toward its ultimate goal of
delivering a mature linear collider design.