The study of complex systems has attracted widespread attention from researchers in the fields of natural sciences, social sciences, and engineering. Prediction is one of the central issues in this field. Although most related studies have focused on prediction methods, research on the predictability of complex systems has received increasing attention across disciplines--aiming to provide theories and tools to address a key question: What are the limits of prediction accuracy? Predictability itself can serve as an important feature for characterizing complex systems, and accurate estimation of predictability can provide a benchmark for the study of prediction algorithms. This allows researchers to clearly identify the gap between current prediction accuracy and theoretical limits, thereby helping them determine whether there is still significant room to improve existing algorithms. More importantly, investigating predictability often requires the development of new theories and methods, which can further inspire the design of more effective algorithms. Over the past few decades, this field has undergone significant evolution. In particular, the rapid development of data science has introduced a wealth of data-driven approaches for understanding and quantifying predictability. This review summarizes representative achievements, integrating both data-driven and mechanistic perspectives. After a brief introduction to the significance of the topic in focus, we will explore three core aspects: the predictability of time series, the predictability of network structures, and the predictability of dynamical processes. Finally, we will provide extensive application examples across various fields and outline open challenges for future research.