Integrated sensing and communications (ISAC) is considered a key enabler to support application scenarios such as the Internet-of-Things (IoT) in which both communications and sensing play significant roles. Multi-carrier waveforms, such as orthogonal frequency division multiplexing (OFDM), have been considered as good candidates for ISAC due to their high communications data rate and good time bandwidth property for sensing. Nevertheless, their high peak-to-average-power-ratio (PAPR) values lead to either performance degradation or an increase in system complexity. This can make OFDM unsuitable for IoT applications with insufficient resources in terms of power, system complexity, hardware size or cost. This article provides IoT-centric constant modulus waveform designs that leverage the advantage of unit PAPR and thus are more suitable in resource-limited scenarios. More specifically, several single-carrier frequency and/or phase-modulated waveforms are considered. A comprehensive discussion on their radar sensing and communications performance is conducted based on performance metrics, including the radar ambiguity function, the bandwidth property, the data rate, and the communications receiver complexity.