Interference temperature (IT) is a widely-used approach for protecting primary users (PUs) from the secondary users (SUs) in underlay cognitive radio. However, when multiple antennas are available at the transmitters and receivers, the spatial structure of the interference comes into play, strongly affecting the performance of the primary network. In this work, we propose interference shaping constraints as an alternative to IT-based approaches. Spatial shaping constraints take account of the structure of interference and exploit it in benefit of the secondary network. Moreover, they can be designed dynamically based on the channel conditions and performance requirements of the PUs. We first show that spatial shaping constraints generalize IT, in that the latter can be expressed as a set of isotropic shaping constraints on each interference dimension. Then, we exemplary consider a PU that has a rate requirement, and propose an algorithm for obtaining suitable shaping matrices, which can be easily modified to include primary transmitter cooperation. This algorithm is performed at the primary receiver using only local channel state information. Afterwards, we address the transceiver optimization of the SU, modeled as a multiple-input multiple-output point-to-point link, and provide optimal and suboptimal transmit covariance designs under the proposed shaping constraints.