Passive radar is an interesting approach in the context of non-cooperative target detection. Because the signal source takes advantage of the so-called illuminator of opportunity (IoO), the deployed system is silent, allowing the operator cheap, portable, and practically undetectable deployments. These systems match perfectly with the use of antenna arrays to take advantage of the additional gains provided by the coherent combination of the signals received at each element. To obtain these benefits, linear processing methods are required to enhance the system’s performance. In this work, we summarize the main beamforming methods in the literature to provide a clear picture of the current state of the art. Next, we perform an analysis of the benefits and drawbacks and explore the chance of increasing the number of antenna elements. Finally, we identify the major challenges to be addressed by researchers in the future.