The 5G and beyond future wireless networks aim to support a large variety of services with increasing demand in terms of data rate and throughput while providing a higher degree of reliability, keeping the overall system complexity affordable. One of the key aspects regarding the physical layer architecture of such systems is the definition of the waveform to be used in the air interface. Such waveforms must be studied and compared in order to choose the most suitable and capable of providing the 5G and beyond services requirements, with flexible resource allocation in time and frequency domains, while providing high spectral and power efficiencies. In this paper, several beyond 5G waveforms candidates are presented, along with their transceiver architectures. Additionally, the associated advantages and disadvantages regarding the use of these transmission techniques are discussed. They are compared in a similar downlink transmission scenario where three main key performance indicators (KPIs) are evaluated. They are the peak-to-average power ratio, the overall system spectral efficiency (wherein the out of band emissions are measured, along with the spectral confinement of the power spectral density of the transmitted signals) and the bit error rate performance. Additionally, other KPIs are discussed.