The Line Emission Mapper (LEM) is a soft-X-ray imaging spectrometer with high spectral
resolution and unprecedented grasp that will bring to light the extended hot-gas halos
that exist around every galaxy. This circumgalactic medium (CGM) is essential to
regulating processes that occur in galaxy evolution but is so tenuous that it is nearly
impossible to see with the current generation of telescopes. LEM's high spectral
resolution, however, will allow us to separate the faint halo emission from the Milkyway
foreground.  This capability also will enable LEM to probe the filamentary intergalactic
medium (IGM) connecting galaxies and galaxy clusters that is the repository of metals
ejected from galaxies over their lifetimes, thereby reading the cosmological history of
galactic feedback.  LEM will measure the kinetics, thermodynamics, and chemistry of hot
diffuse matter on scales from parsecs (supernova remnants), to tens of parsecs
(interstellar medium), to tens of kiloparsecs (CGM), to tens of Megaparsecs (IGM),
covering more than 7 orders of magnitude in length.  LEM is enabled by advanced
technology --- a microcalorimeter spectrometer with 2.5-eV energy resolution (1.3-eV in a
subarray) and 30' field of view paired with an X-ray mirror providing, end to end, >1200
cm^2 effective area at 0.5 keV and 18" spatial resolution, optimized for the 0.2 - 2 keV
band.  These capabilities position LEM to contribute not only to our understanding of
the lifecycles of galaxies and the elements they produce, but also to a wide range of
astrophysical investigations beyond these main science drivers. This talk will present
the context in which this mission has been conceived and proposed, the history on which
it builds, the technology that enables it, and the exciting discovery space that it will
open.