Neuroscientists and Cell Biologists have known for many decades that eukaryotic cells, including neurons, are surrounded by a plasmalemma/axolemma consisting of a phospholipid bilayer that regulates trans-membrane diffusion of ions (including calcium) and other substances. Cells often incur plasmalemmal damage via traumatic injury and various diseases. If the damaged plasmalemma is not rapidly repaired within minutes, activation of apoptotic pathways by calcium influx often results in cell death. We review publications reporting what is less-well known (and not yet covered in neuroscience or cell biology textbooks): that calcium influx at the lesion sites ranging from small nm-sized holes to complete axonal transection activates parallel biochemical pathways that induce vesicles/membrane-bound structures to migrate and interact to restore original barrier properties and eventual reestablishment of the plasmalemma. We assess the reliability of, and problems with, various measures (e.g., membrane voltage, input resistance, current flow, tracer dyes, confocal microscopy, transmission and scanning electron microscopy) used individually and in combination to assess plasmalemmal sealing in various cell types (e.g., invertebrate giant axons, oocytes, hippocampal and other mammalian neurons). We identify controversies such as plug versus patch hypotheses that attempt to account for currently available data on the subcellular mechanisms of plasmalemmal repair/sealing. We describe current research gaps and potential future developments, such as much more extensive correlations of biochemical/biophysical measures with sub-cellular micromorphology. We compare and contrast naturally occurring sealing with recently-discovered artificially-induced plasmalemmal sealing by polyethylene glycol (PEG) that bypasses all natural pathways for membrane repair. We assess other recent developments such as adaptive membrane responses in neighboring cells following injury to an adjacent cell. Finally, we speculate how a better understanding of the mechanisms involved in natural and artificial plasmalemmal sealing is needed to develop better clinical treatments for muscular dystrophies, stroke and other ischemic conditions, and various cancers.