We focus on a broad class of tetragonal itinerant systems sharing a tendency towards the spontaneous formation of incommensurate magnetism with ordering wave vectors Q1,2=(π-δ,0)/(0,π-δ) or Q1,2=(π,δ)/(-δ,π). Employing a Landau approach, we obtain the generic magnetic phase diagram and identify the leading instabilities near the paramagnetic-magnetic transition. Nine distinct magnetic phases exist that either preserve or violate the assumed C4 symmetry of the paramagnetic phase. These are single- and double-Q phases consisting of magnetic stripes, helices, and whirls, either in an individual or coexisting manner. These nine phases can be experimentally distinguished by polarized neutron scattering, or, e.g., by combining measurements of the induced charge order and magnetoelectric coupling. Within two representative five-orbital models, suitable for BaFe2As2 and LaFeAsO, we find that the incommensurate magnetic phases we discuss here are accessible in iron-based superconductors. Our investigation unveils a set of potential candidates for the unidentified C2-symmetric magnetic phase that was recently observed in Ba1-xNaxFe2As2. Among the phases stabilized we find a spin-whirl crystal, which is a textured magnetic C4-symmetric phase. The possible experimental observation of textured magnetic orders in iron-based superconductors opens new directions for realizing intrinsic topological superconductors.