This work investigates the problems of waveform, rectenna and modulation design for far-field Wireless Power Transfer (WPT) and Simultaneous Wireless Information and Power Transfer (SWIPT). A tractable model of the rectenna non-linearity is developed and compared against the linear model, conventionally used in the SWIPT literature. Based on the non-linear model, novel WPT waveforms are formulated and optimized under a power constraint at the transmitter, in order to enhance the output DC power at the rectenna. The waveforms are adaptive to the channel state information (CSI) and are based on multisine signals, which increase the RF-to-DC conversion efficiency of the rectifier. The performance of designed waveforms is evaluated with simulations of practical rectenna circuits in frequency-flat and frequency-selective wireless channels. The rectenna circuits in single- and multiple-diode rectifier configurations are designed and optimized for multisine input signals. The circuit simulations results match the behaviour, predicted by the analytical non-linear rectifier model. It is shown that the waveforms, adaptive to the CSI and designed based on the non-linear model, lead to significant gains in harvested energy over the non-adaptive waveforms and those designed based on the linear model. The gains in harvested energy grow with the number of sinewaves and the number of transmit antennas. A modulation design based on an asymmetric Phase-Shift-Keying (PSK) is presented that improves the SWIPT rate-energy trade-off region significantly. The non-linear rectifier model is adopted for evaluating the output DC power at the energy-harvesting - information-decoding receiver. The harvested energy is maximized under an average power constraint at the transmitter and a constraint on the rate of information transmitted via a multi-carrier OFDM signal over a flat fading channel. The analytical and simulation results demonstrate a significant gain in harvested energy of the optimized asymmetric PSK modulation over the standard symmetric PSK modulation.