Cognitive radio (CR) is an advanced enabling technology for improving the spectrum utilization in wireless systems. Specially, spectrum underlay systems assign licensed bandwidth to a secondary network while guaranteeing the quality of service (QoS) for a primary network. In this paper, we consider downlink CR underlay multiple-input single-output (MISO) networks comprising primary and secondary transmitters serving multiple user. In particular, we formulate the following beamforming optimization problems: 1) total transmit power minimization problem; 2) mean-square error balancing problem; and 3) network interference power minimization problem. In the presence of perfect channel state information (CSI), we formulate the optimization algorithms in a centralized manner and determine the optimal beamformers using standard convex optimization techniques. To account imperfect CSI, we also propose robust algorithms through the worst-case design to mitigate the effect of channel uncertainty. Finally, numerical results are provided to illustrate the validity of our proposed algorithms.