Internet of Things is an integral component of practical future solutions. The integration of intelligence and decision making in objects makes this technology useful for the future generations. However, since this technology makes use of data, it also involves attacks linked to it like data manipulation attacks, leakage attacks, etc. Hence, the research community is exploring ways to enhance the security of these systems which work with IoT in order to maintain its integrity, confidentiality, and secured verification. IoT nodes require a setup which consumes lower computational power than the regular systems and are also economical for variety of applications. However, to maintain the level of security in the system to the advanced level, powerful resources of hardware and software have to be used. Lightweight cryptography rose to prominence as a technology that can guarantee security aspects in the IoT systems. Hence, this paper studies the IoT security model and highlights the security issues within each layer of the model. This review paper discusses the characteristics of LWC and highlights the enhancements that could be brought by LWC integration with IoT. It further presents the recent advancements in this field followed by the future research directions.