The invention includes methods of producing dianhydrosugars. A polyol is reacted in the presence of a first catalyst to form a monocyclic sugar. The monocyclic sugar is transferred to a second reactor where it is converted to a dianhydrosugar alcohol in the presence of a second catalyst. The invention includes a process of forming isosorbide. An initial reaction is conducted at a first temperature in the presence of a solid acid catalyst. The initial reaction involves reacting sorbitol to produce 1,4-sorbitan, 3,6-sorbitan, 2,5-mannitan and 2,5-iditan. Utilizing a second temperature, the 1,4-sorbitan and 3,6-sorbitan are converted to isosorbide. The invention includes a method of purifying isosorbide from a mixture containing isosorbide and at least one additional component. A first distillation removes a first portion of the isosorbide from the mixture. A second distillation is then conducted at a higher temperature to remove a second portion of isosorbide from the mixture.