Short answers, pulled from the story.
The cell membrane is a lipid bilayer composed primarily of phospholipids, along with glycolipids and sterols such as cholesterol. Phospholipids typically account for over 50% of all lipids in plasma membranes, while glycolipids make up about 2%. Proteins constitute roughly half the membrane's volume by weight in most eukaryotic cells.
Gorter and Grendel proposed the lipid bilayer hypothesis in 1925. They extracted lipids from human red blood cells and measured the surface area those lipids covered when spread over water. The area was approximately twice that of the original red blood cells, indicating the membrane consists of two lipid layers.
The fluid mosaic model, published by S. J. Singer and G. L. Nicolson in 1972, describes the cell membrane as a two-dimensional liquid in which lipid and protein molecules diffuse freely. It replaced the earlier paucimolecular model of Davson and Danielli from 1935 and remains the primary framework for understanding membrane structure today.
The cell membrane uses both passive and active transport mechanisms. Small neutral molecules such as oxygen and carbon dioxide cross by diffusion without energy input. Charged and polar molecules are moved through protein channels called permeases or by active transporters that consume cellular energy. Endocytosis engulfs material by forming internal vesicles, while exocytosis releases material by fusing internal vesicles with the plasma membrane.
Cholesterol regulates membrane fluidity by dispersing through the spaces between the hydrophobic tails of membrane lipids. In high temperatures it inhibits fatty acid chain movement, stiffening the membrane. In cold temperatures it acts as antifreeze, preventing lipids from packing too tightly. Cold-weather animals carry more cholesterol in their membranes than warm-weather animals.
For well over 150 years after Robert Hooke described cells in 1665, scientists focused primarily on the cell wall and largely disregarded the membrane. A revision to the cell theory in 1890 acknowledged membranes but treated them as secondary structures. It was not until the early 20th century, through osmosis and permeability experiments, that the significance of the cell membrane was widely accepted.