Scalable Vector Graphics (SVGs) are vital for modern image rendering due to their scalability and versatility. Previous SVG generation methods have focused on curve-based vectorization, lacking semantic understanding, often producing artifacts, and struggling with SVG primitives beyond \textit{path} curves. To address these issues, we introduce StarVector, a multimodal large language model for SVG generation. It performs image vectorization by understanding image semantics and using SVG primitives for compact, precise outputs. Unlike traditional methods, StarVector works directly in the SVG code space, leveraging visual understanding to apply accurate SVG primitives. To train StarVector, we create SVG-Stack, a diverse dataset of 2M samples that enables generalization across vectorization tasks and precise use of primitives like ellipses, polygons, and text. We address challenges in SVG evaluation, showing that pixel-based metrics like MSE fail to capture the unique qualities of vector graphics. We introduce SVG-Bench, a benchmark across 10 datasets, and three tasks: image vectorization, text-driven SVG generation, and diagram generation. Using this contribution, StarVector achieves state-of-the-art performance, producing more compact and semantically rich SVGs.