  A hybrid model is a fibration of a Landau-Ginzburg orbifold over a geometric
base. We study B-type D-branes in hybrid models. Imposing B-type supersymmetry
on the boundary action, we show that D-branes are specified by matrix
factorisations in the fibre direction, together with some geometric data
associated to the base. We also deduce conditions for the compatibility of
these branes with the bulk orbifold actions and R-symmetry. We construct
examples of hybrid B-branes which are generalisations of well-studied branes in
geometric and Landau-Ginzburg models. Hybrid models can arise at limiting
points of the stringy Kahler moduli space of Calabi-Yaus, and can be realised
as phases of the corresponding gauged linear sigma models (GLSMs). Using GLSM
techniques, we establish connections between geometric branes and hybrid
branes. As explicit examples, we consider one- and two-parameter Calabi-Yau
hybrids with a $\mathbb{P}^1$-base.
