Unlike the traditional topology optimization approach that uses the same discretization for finite element analysis and design optimization, this paper proposes a framework for improving multiresolution topology optimization (iMTOP) via multiple distinct discretizations for: (1) finite elements; (2) design variables; and (3) density. This approach leads to high fidelity resolution with a relatively low computational cost. In addition, an adaptive multiresolution topology optimization (AMTOP) procedure is introduced, which consists of selective adjustment and refinement of design variable and density fields. Various two-dimensional and three-dimensional numerical examples demonstrate that the proposed schemes can significantly reduce computational cost in comparison to the existing element-based approach. Copyright © 2012 John Wiley & Sons, Ltd.