Crucial to the physicists’ strong interest in the field is the fact that such macroscopic properties typically arise as the result of a myriad of interactions between the system constituents. Network science aims at simplifying the study of a given complex system by representing it as a network, a collection of nodes and edges interconnecting them. Nowadays, it is widely recognized that some of the structural traits of networks are in fact ubiquitous properties in real systems. The identification and prediction of node influence are of great theoretical and practical significance to be known as a hot research field of complex networks. Most of current research advance is focused on static network or a snapshot of dynamic networks at a certain moment. However, in practical application scenarios, mostly complex networks extracted from society, biology, information, technology are evolving dynamically. Therefore, it is more meaningful to evaluate the node's influence in the dynamic network and predict the future influence of the node, especially before the change of the network structure. In this summary, we contribute on reviewing the improvement of node influence in dynamical networks, which involves three tasks: algorithmic complexity and time bias in growing networks; algorithmic applicability in time varying networks; algorithmic robustness in a dynamical network with small or sharp perturbation. Furthermore, we overview the framework of economic complexity based on dynamical network structure. Lastly, we point out the forefront as well as critical challenges of the field.