Wireless transmission of the recorded neural data without exceeding the extremely-limited available power is one of the most significant challenges in developing implantable brain neural interfaces, particularly for systems with higher channel count. Several data reduction methods such as compressive sensing and adaptive sampling have been proposed in the literature with various levels of success in improving energy efficiency while preserving signal integrity. In this paper, we will review different approaches investigated to address this challenge and will discuss their advantages and disadvantages. We will also discuss the technical viability of an activity-dependent adaptive-resolution fully-dynamic-power direct-ADC neural recording architecture capable of near-loss-less data compression while reducing the required power for both recording and transmission by more than an order of magnitude.