There is an unprecedented need for new treatments for renal failure, as the incidence of this disease is increasing disproportionately to advancements in therapies. Current treatments are limited by the availability of viable organs, for which there is a worldwide lack. These treatment modalities also require a substantial amount of infrastructure, significantly limiting the access to care in most countries. Kidney tissue engineering approaches promise to develop alternative solutions that address many of the inadequacies in current care. Although many advancements have been made—primarily in the past decade—in biofabrication and whole-organ tissue engineering, many challenges remain. One major hindrance to the progress of current tissue engineering approaches is establishing successful vascularization of developed engineered tissue constructs. This review focuses on the recent advancements that address the vascular challenge, including the biofabrication of vasculature, whole-organ engineering through decellularization and recellularization approaches, microscale organogenesis, and vascularization using organoids in the context of kidney tissue engineering. We also highlight the specific challenges that remain in developing successful strategies capable of clinical translation.