Laser-light scattering (LLS) on polar ice, or on polar ice meltwater, is an accepted method for measuring the concentration of water-insoluble aerosol deposits (dust) in the ice. LLS on polar ice can also be used to measure water-soluble aerosols, as well as imperfections (air bubbles and cavities) in the ice. LLS was originally used for measuring the dust concentration in polar ice meltwater, but was later also applied to solid ice for measuring the dust concentration profile along the deep, bubble-free sections of the Greenland Ice Sheet Project 2 (GISP2) ice core from central Greenland. In this paper, we extend the usability of LLS on ice into the realm of the nontransparent, bubbly polar ice, and put previous empirical findings on a theoretical footing. For LLS on clear, bubble-free polar ice, we studied numerically the scattering of light by soluble and insoluble aerosol particles embedded in the ice to complement previous experimental studies. For air bubbles in polar ice, we calculated the effects of multiple light scattering using Mie theory and Monte Carlo simulations, and found a method for determining the bubble size and number concentration using LLS on bubbly ice. We also demonstrated that LLS can be used on bubbly ice to rapidly measure annual layers.