The past 3 decades of thorough scientific scrutiny of carbon nanotubes (CNTs) revealed that, in spite of their remarkable properties, some technological applications are adversely affected by certain difficulties in handling the CNTs, along with their tendencies, arising out of their graphitic structure, to form agglomerates and exhibit limited interaction with other materials. These issues play a crucial role when CNTs are applied as nanofillers inside matrices, in particular polar ones. In this case, unless several preliminary steps are taken, an efficient and uniform dispersion of the CNTs becomes impossible, thus the nanocomposite cannot exhibit the expected final properties. Unfortunately, a universal procedure does not exist since the problem of the dispersion of CNTs is very complex, and its solution requires an advanced understanding of the properties of the CNTs (e.g. whether the CNTs are single- or multiwalled, size, length, lattice defects etc.) as well as of the matrices used. This review aims to help the reader to select the appropriate dispersion procedure by acquiring fundamental knowledge regarding: (1) the synthesis and properties of pristine CNTs; (2) methods of chemical functionalization and properties of functionalized CNTs; and (3) methodologies for the mechanical dispersion of CNTs. A brief overview regarding chemo-physical characterization techniques is also given to enable a better evaluation of the properties of the CNTs, both before and after functionalization.