Matroids combinatorially abstract the ubiquitous notion of "independence" in various contexts such as linear algebra and graph theory.  Recently, an algebro-geometricperspective known as "combinatorial Hodge theory" led by June Huh produced several breakthroughs in matroid theory.  We first give an introduction to matroid theory in this light.  Then, we introduce a new geometric model for matroids that unifies, recovers, and extends various results from previous geometric models of matroids.  We conclude with a glimpse of new questions that further probe the boundary between combinatorics and algebraic geometry.  Joint works with Andrew Berget, Alex Fink, June Huh, Matt Larson, Hunter Spink, and Dennis Tseng.