Carbon nanotubes (CNTs) have lately attracted significant attention in the field of biomedicine. Although a wide repertoire of CNT-based composites has been explored as substrates for cell growth, the fabrication of 3D scaffolds has been more rarely accomplished. Additionally, concerns referred to CNT biocompatibility make their use in biomaterials still controversial. Herein we explore the interaction of three types of CNT-based 3D scaffolds - prepared with multi-walled CNTs and processed to show different architectural and morphological features at the microscale by using three different polymers (i.e., chitosan, chondroitin sulphate and gelatin) - with three types of mammalian cells displaying different sizes and adhesion patterns. Cell-material interaction has been assessed by studying cell viability, adhesion, morphology, and apoptosis. By means of time-lapse confocal laser scanning microscopy, we investigate, for the first time in CNT-based scaffolds, cell migration processes in real time. Scaffolds displaying both a pore size in range with that of cells and lower surface roughness reveal the highest viability values. In contrast, those with a smaller pore size and higher surface roughness account for the lowest cytocompatibility. Results from these studies benefit the fabrication of optimized biomaterials by varying scaffold-dependent parameters in accordance with those of target cells. Furthermore, they may serve to anticipate the response of other cell types sharing similar characteristics to those described herein when in contact with CNT-based scaffolds.