The discovery of graphene and its remarkable and exotic properties have aroused interest in other elements and molecules that form 2D atomic layers, such as metal chalcogenides, transition metal oxides, boron nitride, silicon, and germanium. Silicene and germanene, the Si and Ge counterparts of graphene, have interesting fundamental physical properties with potential applications in technology. For example, researchers expect that silicene will be relatively easy to incorporate within existing silicon-based electronics. In this Account, we summarize the challenges and progress in the field of silicene research. Theoretical calculations have predicted that silicene possesses graphene-like properties such as massless Dirac fermions that carry charge and the quantum spin Hall effect. Researchers are actively exploring the physical and chemical properties of silicene and tailoring it for wide variety of applications. The symmetric buckling in each of the six-membered rings of silicene differentiates it from graphene and imparts a variety of interesting properties with potential technological applications. The pseudo-Jahn-Teller (PJT) distortion breaks the symmetry and leads to the buckling in silicenes. In graphene, the two sublattice structures are equivalent, which does not allow for the opening of the band gap by an external electric field. However, in silicene where the neighboring Si atoms are displaced alternatively perpendicular to the plane, the intrinsic buckling permits a band gap opening in silicene in the presence of external electric field. Silicene's stronger spin orbit coupling than graphene has far reaching applications in spintronic devices. Because silicon prefers sp(3) hybridization over sp(2), hydrogenation is much easier in silicene. The hydrogenation of silicene to form silicane opens the band gap and increases the puckering angle. Lithiation can suppress the pseudo-Jahn-Teller distortion in silicene and hence can flatten silicene's structure while opening the band gap. So far, chemists have not successfully synthesized and characterized a free-standing silicene. But recently chemists have successfully produced silicene sheets and nanoribbons over various substrates such as silver, diboride thin films, and iridium. The supporting substrate critically controls the electronic properties of silicene, and the match of the appropriate support and its use is critical in applications of silicene.