Geological modelling is widely used to predict resource potential in subsurface reservoirs. However, modelling is often slow, requires use of mathematical methods that are unfamiliar to many geoscientists, and is implemented in expert software. We demonstrate here an alternative approach using sketch-based interface and modelling, which allows rapid creation of complex three-dimensional (3D) models from 2D sketches. Sketches, either on vertical cross-sections or in map-view, are converted to 3D surfaces that outline geological interpretations. We propose a suite of geological operators that handle interactions between the surfaces to form a geologically realistic 3D model. These operators deliver the flexibility to sketch a geological model in any order and provide an intuitive framework for geoscientists to rapidly create 3D models. Two case studies are presented, demonstrating scenarios in which different approaches to model sketching are used depending on the geological setting and available data. These case studies show the strengths of sketching with geological operators. Sketched 3D models can be queried visually or quantitatively to provide insights into heterogeneity distribution, facies connectivity or dynamic model behaviour; this information cannot be obtained by sketching in 2D or on paper.