Superconductivity has become a fascinating research field in condensed matter physics since its discovery in 1911. Nowadays, two-dimensional materials exhibit a variety of new physical phenomena, such as Ising superconductivity, topological superconductivity, and unconventional superconductivity. A number of two-dimensional van der Waals crystals exhibit superconductivity, which provide us with a broad research platform for exploring various physical effects and novel phenomena. In this review, we focus our attention on superconducting properties of two-dimensional van der Waals crystals, and highlight the recent progress of the state-of-the-art research on synthesis, characterization, and isolation of single and few layer nanosheets and the assembly of two-dimensional van der Waals superconductors. Finally we conclude the future research directions and prospects in two-dimensional materials with superconductivity.