Deep learning (DL) methodologies have led to significant advancements in various domains, facilitating intricate data analysis and enhancing predictive accuracy and data generation quality through complex algorithms. In materials science, the extensive computational demands associated with high-throughput screening (HTS) techniques such as Density Functional Theory (DFT), coupled with limitations in laboratory production, present substantial challenges for material research. DL techniques are poised to alleviate these challenges by reducing the computational costs of simulating material properties and by generating novel materials with desired attributes. This comprehensive review paper delves into the current state of DL applications in materials design, with a particular emphasis on two-dimensional materials. The article encompasses an in-depth exploration of data-driven approaches in both forward and inverse design within the realm of materials science.