Creating machines capable of understanding the world in 3D is essential in assisting designers that build and edit 3D environments and robots navigating and interacting within a three-dimensional space. Inspired by advances in language and image modeling, we investigate the potential of autoregressive models for a new modality: structured 3D scenes. To this end, we propose a unified LLM framework that aligns language, images, and 3D scenes and provide a detailed ''cookbook'' outlining critical design choices for achieving optimal training and performance addressing key questions related to data representation, modality-specific objectives, and more. We show how to tokenize complex 3D objects to incorporate into our structured 3D scene modality. We evaluate performance across four core 3D tasks -- rendering, recognition, instruction-following, and question-answering -- and four 3D datasets, synthetic and real-world. We show our model's effectiveness on reconstructing complete 3D scenes consisting of complex objects from a single image and on real-world 3D object recognition tasks. Project webpage: https://glab-caltech.github.io/kyvo/