One of the most relevant ways to improve selectivity of sensors based on carbon nanotubes (CNT) is to create hybrid materials with polyaromatic molecules. The interest in hybrid materials is related to the synergistic effect that occurs when the properties of carbon nanomaterials (their one-dimensional electronic structure, high conductivity, large surface area) and properties of polyaromatic molecules (high sensitivity to analytes of different nature, reversibility of the sensor response) are combined. The creation of new porous three-dimensional carbon structures, in which polyaromatic molecules are linkers, is also of interest for creating functional carbon materials of a new generation. This review analyzes the current state of research in the field of hybrid materials based on carbon nanotubes and various polyaromatic molecules (derivatives of phthalocyanine, porphyrin, pyrene, coumarin, BODIPY, etc.) related to the problems of improving the sensitivity and selectivity of chemiresistive and electrochemical sensors. The first part of the review presents an analysis of works that describe various methods of functionalization of carbon nanotubes with aromatic molecules, and examines their influence on the composition and structure of the resulting materials, as well as approaches to creating hybrid 3D structures based on CNTs. The second part of the review is devoted to the functional properties of hybrid materials with the main focus on the analysis of their sensor properties. Examples of the most successful application of hybrid materials as active layers of chemiresistive sensors for determining various gases in the environment are given. When considering the literature data, the main attention is paid to the analysis of the influence of methods of CNT functionalization with polyaromatic molecules on sensor properties. The third part of the review is devoted to the use of hybrid materials for the modification of electrodes of electrochemical sensors for the determination of various molecules in aqueous solutions and biological media.