Slender beams are often employed in engineering materials and structures, with recent advancements in additive manufacturing techniques giving rise to engineered nanolattices and truss architected materials. Despite the significance of understanding the failure modes of these materials, their fracture mechanics is not completely understood and remains an area of ongoing scientific interest. In this talk, we present a novel computational approach for modeling fracture in slender beams subjected to large deformations. We adopt a state-of-the-art geometrically exact Kirchhoff beam formulation to describe the finite deformations of beams in three-dimensions and we model fracture with a discontinuous Galerkin (DG) / cohesive zone model (CZM) computational framework. Our approach is rooted on a discontinuous Galerkin finite element discretization of the beam governing equations, incorporating discontinuities in the position and tangent degrees of freedom at the inter-element boundaries of the finite elements. Prior to fracture initiation, we ensure compatibility of nodal positions and tangents weakly, through the exchange of variationally-consistent forces and moments at the interfaces between adjacent elements. As fracture initiates, these forces and moments transition to cohesive laws modeling interface failure. We present a series of numerical tests to verify and validate our computational framework against a set of benchmarks involving single beams as well as truss geometries.