We show that folding of a non-Newtonian layer resting on a homogeneous Newtonian matrix with finite thickness under influence of gravity can occur by three modes: (1) matrix-controlled folding, dependent on the effective viscosity contrast between layer and matrix, (2) gravity-controlled folding, dependent on the Argand number (the ratio of the stress caused by gravity to the stress caused by shortening), and (3) detachment folding, dependent on the ratio of matrix thickness to layer thickness. We construct a phase diagram that defines the transitions between each of the three folding modes. Our priority is transparency of the analytical derivations (e.g., thin-plate versus thick-plate approximations), which permits complete classification of the folding modes involving a minimum number of dimensionless parameters. Accuracy and sensitivity of the analytical results to model assumptions are investigated. In particular, depth dependence of matrix rheology is only important for folding over a narrow range of material parameters. In contrast, strong depth dependence of the viscosity of the folding layer limits applicability of ductile rheology and leads to a viscoelastic transition. Our theory is applied to estimate the effective thickness of the folded central Asian upper crust using the ratio of topographic wavelength to Moho depth. Phase diagrams based on geometrical parameters show that gravity does not significantly control folding in the Jura and the Zagros Mountains but does control folding in central Asia. Applicability conditions of viscous and thin sheet models for large-scale lithospheric deformation, derived in terms of the Argand number, have implications for the plate-like style of planetary tectonics.