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The rapid progress in artificial intelligence (AI) has been greatly influenced by biological principles, which have inspired techniques such as Deep Learning (DL) and Genetic Algorithms (GAs). Neuroscience-inspired learning focuses not merely on modeling biological neural systems but also on leveraging their mechanisms, such as hierarchical organization, dynamic adaptation, and energy-efficient processing, to improve computational intelligence. The DL model explores the hierarchical and layered architecture of the brain, enabling advances in perception, data analysis, decision-making, and pattern recognition. By contrast, the GAs simulate natural selection, crossover, and mutation to solve complex optimization problems and more, perform global searches across multi-dimensional search spaces. As a result, this review integrates DL and GAs to develop advanced intelligent computing models that emulate biological flexibility and complexity. We highlight the recent developments in bio-inspired DL and GAs, emphasizing biological plausibility, adaptability, and efficiency. The emerging techniques such as Neuroscience-Inspired Deep Learning (NIDL), Neuro-Inspired GAs, Hybrid Neuroevolutionary Workflows (GAs + DL), and Population-Based Reinforcement Learning (PBRL) are discussed. Traditional mechanisms such as Backpropagation, Attention Mechanisms, and Spike-Timing-Dependent Plasticity (STDP) are explored in addition to ideas such as lifelong and adaptive learning, metaplasticity, and memory consolidation, which provide stability and flexibility in dynamic environments. Furthermore, rather than directly comparing Spiking Neural Networks (SNNs) and Convolutional Neural Networks (CNNs), this review contrasts their computational and biological design philosophies. SNNs employ temporal spiking dynamics for event-driven, energy-efficient computation, whereas CNNs perform hierarchical spatial feature extraction characteristic of modern DL. We also explore neuroevolutionary methods, such as NeuroEvolution of Augmenting Topologies (NEAT) and Genetic CNNs. Neuroscience-motivated learning extends beyond biological modelling to harness heterogeneous neural principles across domains such as robotics, medicine, and signal processing. This survey delineates NIDL-GA synergy, their limits, and areas of future work in neuromorphic computing, explainable AI, and biologically inspired lifelong learning. Collectively, these paradigms hold the promise of next-generation AI systems to be robust, interpretable, and adaptable in real time.