The human brain is a complex organ responsible for controlling bi-directional signals between the peripheral and central nervous systems through a complex network of neurons. Despite significant research efforts, many brain diseases and disorders remain poorly understood, and effective treatments are lacking. Recent advances in neurotechnology, including bioelectronic devices that can record and stimulate neural activity in the brain, have played a crucial role in addressing these challenges. However, conventional bioelectronic devices face significant challenges due to the mechanical mismatch between soft brain tissue and the rigid electrode. This review paper discusses the limitations of conventional bioelectronics to record brain neural activity and emphasizes the importance of the mechanical properties of device materials and dimensionality. Furthermore, it highlights the latest research on different types of bioelectronic technologies, including flexible, stretchable, and intrinsically soft bioelectronic devices available for monitoring and modulating brain activity and their advantages and limitations. By highlighting recent advancements and exploring potential future developments, this review paper provides a comprehensive overview of the current state of the art in flexible and stretchable bioelectronic technology for brain monitoring and therapeutic application.