Concrete is the most common building material; therefore, when designing structures, it is obligatory to consider all structural parameters and design characteristics such as acoustic properties. In particular, this is to ensure comfortable living conditions for people in residential premises, including acoustic comfort. Different types of concrete behave differently as a sound conductor; especially dense mixtures are superior sound reflectors, and light ones are sound absorbers. It is found that the level of sound reflection in modified concrete is highly dependent on the type of aggregates, size and distribution of pores, and changes in concrete mix design constituents. The sound absorption of acoustic insulation concrete (AIC) can be improved by forming open pores in concrete matrices by either using a porous aggregate or foam agent. To this end, this article reviews the noise and sound transmission in buildings, types of acoustic insulating materials, and the AIC properties. This literature study also provides a critical review on the type of concretes, the acoustic insulation of buildings and their components, the assessment of sound insulation of structures, as well as synopsizes the research development trends to generate comprehensive insights into the potential applications of AIC as applicable material to mitigate noise pollution for increase productivity, health, and well-being.