Recent advances in the development of intra-cortical neural interfacing devices show the bright horizon of having access to brain-implantable microsystems with extremely high channel counts in the not-so-distant future. With the fabrication of high-density neural interfacing microelectrode arrays, the handling of the neural signals recorded from the brain is becoming the bottleneck in the realization of next generation wireless brain-implantable microsystems with thousands of parallel channels. Even though a spectrum of engineering efforts has been reported for this purpose at both system and circuit levels, it is now apparent that the most effective solution is to resolve this problem at the signal level. Employment of digital signal processing techniques for data reduction or compression has therefore become an inseparable part of the design of a high-density neural recording brain implant. This paper first addresses technical and technological challenges of transferring massive amount of recorded data off high-density neural recording brain implants. It then provides an overview of the 'on-implant signal processing' techniques that have been employed to successfully stream neuronal activities off the brain. What distinguishes this class of signal processing from signal processing in general is the critical importance of hardware efficiency in the implementation of such techniques in terms of power consumption, circuit size, and real-time operation. The focus of this review is on spike detection and extraction, temporal and spatial neural signal compression, and spike sorting.