Large Eddy Simulations (LES) of vertical convective vortices and dust devils in the terrestrial Convective Boundary Layer (CBL) are presented. A CBL-scale simulation and a dust-devil-scale simulation are preformed at different resolutions. The CBL-scale simulation is performed to study the generation of vertical vortices and the dust-devil-scale simulation is performed to study the detailed structures and stages of dust devil development. The simulation results show that dust devils undergo three stages of development as the swirl ratio increases: a weak vortex stage, a single-celled vortex stage and a two-celled vortex stage. The structure of a dust devil can be divided into four regions: outflow, core, corner and inflow layer. The different structures and characteristics of the modelled dust devil during various stages of development and the influence of the surface on the dust devil profile are described using some of the simulation results as illustrations. The causes of the different structures and characteristics are analysed through the interplay between the rotation, the radial pressure gradient, the buoyancy and the axial pressure gradient. Dust devils are a type of concentrated vortex similar to tornadoes. The differences in the structure and characteristics of tornadoes and the modelled dust devils are discussed in this paper. The carrying aloft of sand particles within the modelled dust devil is explored using a Lagrangian coordinate system. Sand particles can be transported by the updraft with particles of varying diameters follow different tracks.