  We construct various modular compactifications of the space of elliptic K3
surfaces using tools from the minimal model program, and explicitly describe
the surfaces parametrized by their boundaries. The coarse spaces of our
constructed compactifications admit morphisms to the Satake-Baily-Borel
compactification. Finally, we show that one of our spaces is smooth with coarse
space the GIT quotient of pairs of Weierstrass K3 surfaces with a chosen fiber.
