Multiple-input multi-output (MIMO), emerged as one of the most significant breakthroughs inwireless communications theory over the last two decades, is considered as a key tomeeting the increasing demands for high data rates and mass wireless access services over a limited spectrum bandwidth. Transmit beamforming with receive combining is a low-complexity technique to exploit the benefits of MIMO wireless systems. It has received much interest over the last few years, because it provides substantial performance improvement without sophisticated signal processing. In order to enable the beamforming operation, either full or partial channel state information (CSI) has to be furnished to the transmitter. With full CSI, the optimal transmit beamforming scheme is maximum ratio transmission (MRT) [Dighe et al. (2003a)], where the principal right singular vector of the channel matrix is used as the beamforming vector. In Rayleigh fading, exact expressions for the symbol error rate (SER) of MRT were derived in [Dighe et al. (2003a;b)], and the asymptotic error performance was studied in [Zhou & Dai (2006)]. However, in certain application scenarios, e.g. frequency division duplex (FDD) systems, CSI is not usually available at the transmitter. To cope with the lack of CSI, a beamforming scheme based on finite-rate feedback has been proposed in the literature, where the CSI is quantized at the receiver and fed back to the transmitter. This scheme has been adopted in current 3GPP specifications. Under the assumption of independent block-fading and the assumption of delayand error-free feedback, the design and performance analysis of quantized beamforming systems have been well investigated. Different beamformer design methods were developed in [Mukkavilli et al. (2003); Love & Heath (2003); Xia & Giannakis (2006)]. In multiple-input single-output (MISO) cases, lower bounds to the outage probability and symbol error rate (SER) were derived in [Mukkavilli et al. (2003)] and [Zhou et al. (2005)], respectively. In MIMO cases, the average receive signal-to-noise ratio (SNR) and outage probability were studied in [Mondal & Heath (2006)]. Analytical results showed that full diversity order can be achieved by a well-designed beamformer [Love & Heath (2005)]. This chapter highlights recent advances in beamforming based on finite-rate feedback from a communication-theoretic perspective. We first study the SER performance when the feedback link is delayand error-free. Then non-ideal factors in the feedback link are investigated, and countermeasures are proposed to compensate the performance degradation due to non-ideal feedback. 12