Interest and investment in AI research is at a historical peak. Yet, despite the performance obtained, current artificial intelligence systems have adopted a narrow approach with distinct limitations. One source of these limitations is the reliance on extrinsic learning mechanisms, with gradient descent and its variants serving as the primary means of model optimization. However, intelligent systems arising from biological brains display intrinsic learning through integrated processes. Since biological brains operate with power and data efficiencies otherwise unparalleled, along with the capability for rapid real-time adaption, it may be beneficial to reconsider neural systems in the current search for AI. There are two mutually inclusive possibilities this may take: (1) using biological cells as the substrate for information processing and intelligence; (2) developing new AI algorithms inspired by these biological systems. In either of these cases, exploiting synthetic biological methods to explore the underlying mechanisms of how neural systems process information and exhibit intelligence will be necessary. By reviewing a recent proof-of-concept for Synthetic Biological Intelligence and the corresponding implications in this context, potential methods for both these possibilities are discussed. Ultimately, this work aims to encourage drawing inspiration from natural intelligence to foster more robust, efficient, and adaptive AI.