Volumetric 3D printing enables the rapid fabrication of centimetre-scale objects, with the fastest techniques requiring only a few seconds. Having emerged during the past 7 years, this new family of technologies is posed to revolutionize additive manufacturing, fabricating objects and functional parts in a layerless fashion directly within a vat of material in response to optical and acoustic fields. Modern volumetric 3D printing methods are overcoming many challenges inherent to conventional layer-by-layer approaches, the standard in research and industry for the past 40 years. This Review focuses on identifying upcoming challenges and research directions in materials chemistry and process engineering to move volumetric 3D printing from its infancy to its broader adoption. Recent advances include the development of techniques based on optical tomography, light and acoustic holography, xolography, multiwavelength and upconversion-mediated printing, as well as the introduction of materials with custom-designed properties. Promising applications in the development of optical and photonic components, rapid prototyping, soft robotics and bioprinting of living cells are discussed along with a vision for the evolution of volumetric manufacturing towards a broadly accessible technology platform.