The main drawback of phase change materials (PCMs) is their low thermal conductivity, which limits the possibilities of a wide range of implementations. Therefore, the researchers, as found in the literature, proposed several methods to improve the thermal conductivity of PCMs, including inserting high thermal conductivity materials in nano-, micro-, and macro-scales, as well as encapsulation of PCMs. However, these inserts impact the other properties of PCMs like latent heat, melting temperature, thermal stability, and cycling stability. Hence, this paper aims to review the available in the open literature research on the main properties of enhanced PCMs that undergo solid–liquid transition. It is found that inserting high thermal conductivity materials and encapsulation results in improved thermal conductivity of PCMs, but it decreases their latent heat. Moreover, the insertions can act as nucleating agents, and the supercooling degree can be reduced. Some of the thermal conductivity enhancers (TCEs) may prevent PCMs from leakage. However, some test results are inconsistent and some seem to be questionable. Therefore, this review indicates these discrepancies and gaps in knowledge and points out possible directions for further research.