Monolithic three-dimensional (M3D) integration represents a transformative approach in semiconductor technology, enabling the vertical integration of diverse functionalities within a single chip. This review explores the evolution of M3D integration from traditional bulk semiconductors to low-dimensional materials like two-dimensioanl (2D) transition metal dichalcogenides (TMDCs) and carbon nanotubes (CNTs). Key applications include logic circuits, static random access memory (SRAM), resistive random access memory (RRAM), sensors, optoelectronics, and artificial intelligence (AI) processing. M3D integration enhances device performance by reducing footprint, improving power efficiency, and alleviating the von Neumann bottleneck. The integration of 2D materials in M3D structures demonstrates significant advancements in terms of scalability, energy efficiency, and functional diversity. Challenges in manufacturing and scaling are discussed, along with prospects for future research directions. Overall, the M3D integration with low-dimensional materials presents a promising pathway for the development of next-generation electronic devices and systems.