In this talk, optimization techniques for the design of broadband beamforming system are discussed. In many applications, it is important to deploy many sensors for data collection and to allow sensors to integrate as a complete system. For acoustic applications, microphone arrays together with beamforming techniques can be applied. Here, we review various approaches and discuss some of the performance issues. We will discuss some advances in the optimal design of multi-dimensional broadband beamforming system. Different optimization models will be considered. In addition to optimizing filter coefficients, we discuss how to optimize on the geometric configuration of the array via as a non-convex optimization problem. We show that better beamformers can be designed via optimization techniques. We illustrate the proposed method by several novel designs.