In situ observations in Earth’s and Saturn’s magnetosheaths and in the solar wind reveal the Alfvén vortices as intermittent structures whose scales range from fluid lengths down to a few ion lengths. We develop a new model of magnetic vortices in high-beta plasmas, possessing compressible density and magnetic field, whose typical size goes from fluid to ion scales. At magnetofluid scales, we find nonpropagating field-aligned cylindrical monopoles and inclined propagating dipoles. Their transverse magnetic and velocity fluctuations are aligned, but not identical, and they exhibit density and compressible magnetic field fluctuations localized inside the vortex core. At ion or kinetic scales (with the smallest radii and in the absence of acoustic perturbations, only dipolar Alfvén vortices survive with properties similar to those at fluid scales, except that $\frac{\delta n}{n_0}$ reaches the level of $\frac{dB}{B_0}$.We also find pressure-balanced kinetic slow magnetosonic dipoles, possessing finite parallel electric field and purely compressional magnetic field perturbation, whose existence is facilitated by a strong ion temperature anisotropy.