Wireless communications are currently faced with two main challenges. The first challenge stems from the enormous number of Internet of Things (IoT) devices that transmit very small amounts of data. The second challenge is the need for ever-increasing data rates required by users of multimedia rich services, as well as the extremely low latency required in emerging applications such as autonomous vehicles and augmented reality. In this thesis we deal with important physical layer (PHY) aspects that have not been analyzed in-depth in the existing literature, and whose study can help to address the aforementioned challenges. Low-power wide-area networks (LPWANs) comprise a big part of the IoT. For energy efficiency reasons, most of LPWAN technologies adopt uncoordinated channel access schemes which result in collisions. This issue becomes more severe as the number of devices increases, putting the scalability of LPWANs at risk as they become interference-limited. To evaluate and support LPWAN scalability, in the first part of this thesis we perform a thorough analysis of the performance of one of the most important LPWAN technologies, namely LoRa. We analyze the LoRa performance in interference scenarios, and we derive expressions, as well as very accurate low-complexity approximations, for the error rate of LoRa for both the uncoded and coded cases, and with carrier frequency offset (CFO). We also propose and analyze the coherent demodulation of LoRa under interference, as a potential receiver improvement in collision scenarios. Finally, we build a standard-compatible LoRa PHY software-defined radio (SDR) prototype based on GNU Radio, which can be used for measurements of LoRa PHY performance. The second part of this thesis focuses on full-duplex radios, which allow simultaneous transmission and reception in the same frequency band, and have been proposed as a possible solution to overcome the capacity bottleneck of high data-rate applications. However, full-duplex transceivers suffer from strong self-interference. Perfect self-interference cancellation is difficult to achieve due to the presence of strong non-linear signal components, which are introduced by hardware imperfections inherent in the transmitter and receiver chains. We propose the digital predistortion of the transmit signal to compensate for the cascade of the transceiver non-linearities and enhance self-interference cancellation. Unfortunately, a residual self-interference component always remains, particularly when operating at realistic transmit powers. To increase the usefulness of full-duplex technology, we examine communication schemes where using full-duplex transceivers can significantly improve the performance in terms of both throughput and latency, even under imperfect self-interference suppression. In particular, we examine the use of full-duplex technology in cognitive radios, and in communication links with asymmetric capacity requirements between the uplink and downlink channels.