With the rapid development of the Internet of Things (IoT), security of constrained devices suffer a serious challenge. LightWeight Cryptography (LWC) as the main security measure of constrained devices is getting more and more attention of researchers. The recent advance in issues of lightweight cryptography such as design strategy, security and performance were reviewed. Firstly, design strategies and the key issues during the design were elaborated, and many aspects such as principle and implementation mechanisms of some typical and common lightweight cryptography were analyzed and discussed. Then not only the commonly used cryptanalysis methods were summarized but also the threat of side channel attacks and the issues should be noted when adding resistant mechanism were emphasized. Furthermore, detailed comparison and analysis of the existing lightweight cryptography from the perspective of the important indicators of the performance of lightweight cryptography were made, and the suitable environments of hardware-oriented and software-oriented lightweight cryptography were given. Finally, some unresolved difficult issues in the current and possible development direction in the future of lightweight cryptography research were pointed out. Considering characteristics of lightweight cryptography and its application environment, comprehensive assessment of security and performance will be the issues which worth depth researching in the future.