The resource-constrained project scheduling problem(RCPSP) under uncertainty is to study the arrangement of activities with limited resources under the uncertain environment so as to optimize certain objectives. The RCPSP under uncertainty is of strong engineering background, which has great research significance in both the academic and the application fields. The problem has the complexities such as large scale, strong constraint, multiple local minima, multiple objective and uncertainty, which make it very difficult to be solved. Thus, the mathematical description of the RCPSP under uncertainty and some of its specific forms are introduced, and the advances in algorithms for the RCPSP under uncertainty are reviewed, and some related applications are summarized. Finally, some future research directions and contents are pointed out.