© 2016 IOP Publishing Ltd. The rise of two-dimensional (2D) materials research took place following the isolation of graphene in 2004. These new 2D materials include transition metal dichalcogenides, mono-elemental 2D sheets, and several carbide- and nitride-based materials. The number of publications related to these emerging materials has been drastically increasing over the last five years. Thus, through this comprehensive review, we aim to discuss the most recent groundbreaking discoveries as well as emerging opportunities and remaining challenges. This review starts out by delving into the improved methods of producing these new 2D materials via controlled exfoliation, metal organic chemical vapor deposition, and wet chemical means. We look into recent studies of doping as well as the optical properties of 2D materials and their heterostructures. Recent advances towards applications of these materials in 2D electronics are also reviewed, and include the tunnel MOSFET and ways to reduce the contact resistance for fabricating high-quality devices. Finally, several unique and innovative applications recently explored are discussed as well as perspectives of this exciting and fast moving field.