With tremendous progress of graphene and with the consideration of the compatibility with semiconductor industry, the construction of analogous two-dimensional crystalline systems-new two-dimensional honeycomb and layered materials composed of elements other than carbon, the group IV (Si, Ge) analogs of graphene and the investigation of their fascinated electronic properties have become the frontier topics of condensed matter physics. Theoretical calculation predicts that unlike the planar structure of graphene, the germanene has stable, two-dimensional, low-buckled, honeycomb structure similar to that of silicene, but has much higher spin-orbit band gap than silicene, which is certainly of crucial importance in future electronics. The influences of atomic structures and the buckling of the low-buckled geometry on local electronic structure of the fabricated germanene are also reviewed from the atomic point of view. As theoretical studies on germanene are rapidly increasing, now the major challenge in this field is the preparation of high-quality germanene. Compared with silicene, the germanene has larger Ge-Ge interatomic distance which can weaken the orbital overlaps, resulting in the big difficulty in constructing germanene. In this work we review the recent progress of experimental epitaxial growth of germanene on surfaces, with emphasis on metal surfaces. The growth of quasi-freestanding germanene and its potential applications in nanoelectronics in the future are also discussed.