The intelligence behind robotic arms has evolved significantly, incorporating advanced methodologies from kinematics to brain-computer interfaces. This review critically examines the sequential steps in robotic arm control, covering Kinematic Analysis, Path Planning, Trajectory Optimization, and various Control Techniques, with a particular focus on Brain Signal Acquisition and Classification Approaches. While substantial progress has been made, key challenges persist. Traditional kinematic models often struggle with real-world uncertainties, computational inefficiencies, and singularity issues, limiting adaptability in dynamic environments. Path planning and trajectory optimization face constraints in real-time applications, where trade-offs between accuracy, computational speed, and obstacle avoidance remain critical. Control methodologies, from classical techniques to AI-driven approaches, must enhance robustness and energy efficiency to ensure stability in practical deployments. Furthermore, brain-controlled robotic arms, despite promising breakthroughs, contend with signal variability, low resolution, and the need for extensive training, raising concerns about reliability, ethical implications, and data privacy. This review consolidates recent advancements while addressing the fundamental challenges impeding seamless integration in industrial and biomedical applications. By bridging these gaps, future research can refine robotic arm intelligence, fostering more autonomous, precise, and human-integrated systems.