Endocytic budding implies the remodeling of a plasma membrane portion from a flat sheet to a closed vesicle. Clathrin- and actin-mediated endocytosis in yeast has proven a very powerful model to study this process, with more than 60 evolutionarily conserved proteins involved in fashioning primary endocytic vesicles. Major progress in the field has been made during the last decades by defining the sequential recruitment of the endocytic machinery at the cell cortex using live-cell fluorescence microscopy. Higher spatial resolution has been recently achieved by developing time-resolved electron microscopy methods, allowing for the first time the visualization of changes in the plasma membrane shape, coupled to the dynamics of the endocytic machinery. Here, we highlight these advances and review recent findings from yeast and mammals that have increased our understanding of where and how endocytic proteins may apply force to remodel the plasma membrane during different stages of the process.