Cellular systems are interference limited in nature. This problem is further accentuated in upcoming commercial wireless standards, which intend to use all the available spectrum in every cell in the network to improve peak data rates. This, however, could lead to considerable interference among neighboring cells, decreasing data rates and causing outages at the cell-edge. Multicell cooperation offers a solution for reducing the high levels of interference. The basic idea is that base stations coordinate transmissions by sharing user information among themselves via backhaul links. With the backhaul being bandwidth limited, cooperative strategies that involve the exchange of only user channel state information (CSI) among base stations offer the best tradeoff between complexity, backhaul load and performance gains. This dissertation focuses on these partial cooperative techniques, known as coordinated beamforming in 3GPP LTE Advanced. In existing frequency division duplex systems, users estimate and feedback the CSI of a single channel over a finite-bandwidth feedback link, using limited feedback techniques. In a multicell cooperative scenario, each user needs to transmit the CSI of multiple channels using the same feedback link. This implies that the available feedback bandwidth must be efficiently shared among different channels to maximize performance gains in the cellular network. This dissertation develops three different approaches to limited feedback in multicell cooperative systems. The first technique, separate quantization, involves each channel being fed back individually using a different codebook. Closed-form expressions are derived to partition adaptively the available feedback bits, as a function of the signal strengths and delays associated with each of the multiple channels. The second strategy is known as joint quantization, where the CSI of all the channels are quantized together as a composite vector. It is shown that though this approach yields higher data rates with smaller feedback requirements than separate quantization, it requires the design and storage of special codebooks. Finally, predictive joint quantization is proposed to exploit the temporal correlation of the wireless channel to reduce feedback requirements significantly as compared to the other two strategies, at the cost of high complexity at the user terminals.