Adaptive antenna arrays have become the system of choice for protecting Global Navigation Satellite Systems (GNSS) receivers in strong radio frequency interference environments. GNSS receiver adaptive antenna arrays have small aperture (of the order of a wavelength) and few (e.g., less than 10) elements. In the near future, even smaller vehicles will be equipped with protected GNSS receivers. Therefore, future GNSS receiver antenna arrays will be even smaller in size. At the same time, requirements for availability, accuracy, and integrity monitoring will increase. Novel array signal processing techniques need to be developed and deployed to meet these requirements. This paper presents state-of-the-art GNSS adaptive antenna array signal processing techniques. Some drawbacks of the current GNSS antenna signal processing techniques are also discussed in this paper, and new ideas for further research and development in GNSS adaptive antennas are presented.