Research on two-dimensional (2D) materials has been explosively increasing in last seventeen years in varying subjects including condensed matter physics, electronic engineering, materials science, and chemistry since the mechanical exfoliation of graphene in 2004. Starting from graphene, 2D materials now have become a big family with numerous members and diverse categories. The unique structural features and physicochemical properties of 2D materials make them one class of the most appealing candidates for a wide range of potential applications. In particular, we have seen some major breakthroughs made in the field of 2D materials in last five years not only in developing novel synthetic methods and exploring new structures/properties but also in identifying innovative applications and pushing forward commercialisation. In this review, we provide a critical summary on the recent progress made in the field of 2D materials with a particular focus on last five years. After a brief background introduction, we first discuss the major synthetic methods for 2D materials, including the mechanical exfoliation, liquid exfoliation, vapor phase deposition, and wet-chemical synthesis as well as phase engineering of 2D materials belonging to the field of phase engineering of nanomaterials (PEN). We then introduce the superconducting/optical/magnetic properties and chirality of 2D materials along with newly emerging magic angle 2D superlattices. Following that, the promising applications of 2D materials in electronics, optoelectronics, catalysis, energy storage, solar cells, biomedicine, sensors, environments, etc. are described sequentially. Thereafter, we present the theoretic calculations and simulations of 2D materials. Finally, after concluding the current progress, we provide some personal discussions on the existing challenges and future outlooks in this rapidly developing field.