Endocytosis is an essential eukaryotic process that maintains the homeostasis of the plasma membrane proteome by vesicle-mediated internalization. Its predominant mode of operation utilizes the polymerization of the scaffold protein clathrin forming a coat around the vesicle; therefore, it is termed clathrin-mediated endocytosis (CME). Throughout evolution, the machinery that mediates CME is marked by losses, multiplications, and innovations. CME employs a limited number of conserved structural domains and folds, whose assembly and connections are species dependent. In plants, many of the domains are grouped into an ancient multimeric complex, the TPLATE complex, which occupies a central position as an interaction hub for the endocytic machinery. In this review, we provide an overview of the current knowledge regarding the structural aspects of plant CME, and we draw comparisons to other model systems. To do so, we have taken advantage of recent developments with respect to artificial intelligence-based protein structure prediction.