Graft incompatibility is a poorly understood phenomenon that presents a severe agricultural challenge. Unlike immediate incompatibility that results in rapid death, delayed incompatibility can take months or even years to manifest, creating a significant problem for perennial crop production. To investigate graft compatibility, we utilized the Solanaceae family due to its agriculturally relevant grafted crops, short life cycles and small stature. Additionally, Solanaceae contains within it a model species, Solanum lycopersium (tomato), which possesses a suite of genetic tools such as a sequenced genome and efficient transformation protocol. To first understand graft compatibility within Solanaceae, we performed a reciprocal graft trial with 4 economically relevant crops and found that most of these heterografts are capable of surviving but are incompatible due to failed vascular reconnections. Next, we utilized a novel model system: Solanum lycopersicum (tomato) and Capsicum annuum (pepper) to investigate delayed graft incompatibility. We employed classical techniques such as vascular staining and physiological measurements as well as more computational approaches to explore the temporal, genetic, and anatomical components involved in grafting. We inferred gene regulatory networks for compatible self-grafts versus incompatible heterografts and predicted core regulators for grafting. We then examined the role of vascular development in graft formation and validated SlWOX4 as a regulator for grafting in tomato. Finally, we studied how graft compatibility influences cell death, by utilizing viability stains and programmed cell death indicators. We were able to show that programmed cell death is present in all graft junctions, but that the driving cause for cell death in this incompatible combination is acute stress-induced necrosis. This work has explored the symptoms, causes, and taxonomic limits of graft compatibility. We have identified novel genes involved in grafting and identified a role for necrosis in graft-incompatibility, further elucidating the mechanisms that underlie plant grafting.