The chemically functionalized carbon nanotubes (f-CNTs) and hydrogen bonding modified polymer composites (CPCs) exhibit unique chemical, mechanical, electrical, and thermal properties and are emerging as promising materials to achieve extraordinarily high electrical and thermal conductivity, lightweight and anticorrosion, superior strength and stiffness for potential applications in the aerospace and automotive industries, energy conversion, and optical and electronic devices, therefore, attracting considerable research efforts over the past decade. In this review, the fundamentals of the topics on f-CNTs, hydrogen bonding, and CNT directional alignment have been briefly introduced. The research on the electrical, thermal, and mechanical properties have been reviewed. The effects of the CNT morphology, hydrogen bonding, CNT alignment and aspect ratio, and the interactions between the constitutes on the CPC performance is critical to understand the fundamentals and challenges of designing such materials with desired properties and their potential applications. However, to gain a comprehensive and quantitative understanding of the effects of these factors on the performance of CPCs, further studies by computer modeling, especially MD simulations, will be highly needed for effective new/novel material design and development. <strong><br> </strong>