Communication security of an Internet-of-Things (IoT) product depends on the variety of protocols employed throughout its lifetime. The underlying low-power radio communication technologies impose constraints on maximum transmission units and data rates. Surpassing maximum transmission unit thresholds has an important effect on the efficiency of the solution: transmitting multiple fragments over lowpower IoT radio technologies is often prohibitively expensive. Furthermore, IoT communication paradigms such as one-to-many require novel solutions to support the applications executing on constrained devices. Over the last decade, the Internet Engineering Task Force (IETF) has been working through its various Working Groups on defining lightweight protocols for Internet-of-Things use cases. ''Lightweight'' refers to the minimal processing overhead, memory footprint and number of bytes in the air, compared to the protocol counterparts used for non-constrained devices in the Internet. This article overviews the standardization efforts in the IETF on lightweight communication security protocols. It introduces EDHOC, a key exchange protocol, OSCORE and Group OSCORE, application data protection protocols adapted for securing IoT applications. The article additionally highlights the design considerations taken into account during the design of these protocols, an aspect not present in the standards documents. Finally, we present an evaluation of these protocols in terms of the message sizes and compare with the non-constrained counterpart, the (D)TLS protocol. We demonstrate that the novel key exchange protocol EDHOC achieves ×5 reduction over DTLS 1.3 authenticated with pre-shared keys in terms of total number of bytes transmitted over the air, while keeping the benefits of authentication with asymmetric credentials.