Sub-millimeter scale three-dimensional (3D) structures are disclosed with customizable chemical properties and/or functionality. The 3D structures are referred to as drop-carrier particles. The drop-carrier particles allow the selective association of one solution (i.e., a dispersed phased) with an interior portion of each of the drop-carrier particles, while a second non-miscible solution (i.e., a continuous phase) associates with an exterior portion of each of the drop-carrier particles due to the specific chemical and/or physical properties of the interior and exterior regions of the drop-carrier particles. The combined drop-carrier particle with the dispersed phase contained therein is referred to as a particle-drop. The selective association results in compartmentalization of the dispersed phase solution into sub-microliter-sized volumes contained in the drop-carrier particles. The compartmentalized volumes can be used for single-molecule assays as well as single-cell, and other single-entity assays.