Cells contain thousands of different lipids. Their rapid and redundant metabolism, dynamic movement, and many interactions with other biomolecules have justly earned lipids a reputation as a vexing class of molecules to understand. Further, as the cell's hydrophobic metabolites, lipids assemble into supramolecular structures─most commonly bilayers, or membranes─from which they carry out myriad biological functions. Motivated by this daunting complexity, researchers across disciplines are bringing order to the seeming chaos of biological lipids and membranes. Here, we formalize these efforts as "synthetic lipid biology". Inspired by the idea, central to synthetic biology, that our abilities to understand and build biological systems are intimately connected, we organize studies and approaches across numerous fields to create, manipulate, and analyze lipids and biomembranes. These include construction of lipids and membranes from scratch using chemical and chemoenzymatic synthesis, editing of pre-existing membranes using optogenetics and protein engineering, detection of lipid metabolism and transport using bioorthogonal chemistry, and probing of lipid-protein interactions and membrane biophysical properties. What emerges is a portrait of an incipient field where chemists, biologists, physicists, and engineers work together in proximity─like lipids themselves─to build a clearer description of the properties, behaviors, and functions of lipids and membranes.