Bipedal robots, designed to replicate human locomotion, face significant balance challenges due to instability and high degrees of freedom. This study examines dynamical models, balance control strategies, and locomotion methodologies. Dynamical models are categorized into simplified, centroidal dynamics, and whole-body dynamics models. Simplified models, such as the Linear Inverted Pendulum Model (LIPM), approximate the robot as a point mass at the Center of Mass (CoM) but neglect upper-body dynamics and complex terrain interactions. Centroidal dynamics models incorporate CoM motion, contact forces, and angular momentum for improved disturbance rejection but require extensive computational resources. Whole-body models achieve high fidelity by integrating joint torques and external forces but are constrained by computational complexity. Balance control methods for standing bipedal robots are classified into joint-specific and whole-body approaches. Ankle and hip strategies address small perturbations but are insufficient for real-world disturbances. Whole-body control utilizes all body segments to modulate contact forces and regulate momentum, enhancing stability against external disturbances, though challenges remain in force modeling and state estimation. Locomotion control is divided into model-based and learning-based approaches. Model-based strategies include LIPM and its extensions-based methods, Zero Moment Point (ZMP)-based methods, which ensure dynamic stability by maintaining moments within the support polygon; Capture Point (CP)-based methods, which predict foot placement to prevent falls; and Divergent Component of Motion (DCM)-based approaches, which adjust footsteps based on CoM divergence. While learning-based methods leverage Reinforcement Learning (RL) and human motion data for adaptive and energy-efficient gait generation. This study highlights challenges in energy efficiency, terrain adaptation, and scalability, proposing sensor fusion, energy-aware RL reward functions, and hierarchical control architectures as potential solutions.