Internet of Things (IoT) is a promising technology for creating smart environments, smart systems, and smart services. Since security is a fundamental requirement of IoT platforms, solutions that can provide both encryption and authenticity simultaneously have recently attracted much attention from academia and industry. This article analyses in detail state-of-the-art lightweight authenticated encryption (LAE) targeted to IoT systems. This work provides a thorough description of the algorithms, and the study systematically classifies them to facilitate understanding of relevant intricacies of the schemes. Among reviewed algorithms, there is a trade-off to retain design security, resources cost, and efficient performance. ACORN is the effective scheme on various platforms in terms of utilization of resources and power consumption, while MORUS and AES-CLOC are the fastest in hardware platforms. However, they are susceptible to misuse despite their resistance to side channel attacks. In contrast, JOLTICK, PRIMATESs, COLM, DeoxysII, OCB, and AES-JAMBU are provably resistant to nonce misuse. The challenges for possible future research are summarized. Overall, the article provides researchers and developers with practical guidance on various design aspects and limitations as well as open research challenges in the current lightweight authenticated encryption for IoT.