This article gives an overview of the current progress of a class of supramolecular soft materials consisting of fiber networks and the trapped liquid. After discussing the up-to-date knowledge on the types of fiber networks and the correlation to the rheological properties, the gelation mechanism turns out to be one of the key subjects for this review. In this concern, the following two aspects will be focused upon: the single fiber network formation and the multi-domain fiber network formation of this type of material. Concerning the fiber network formation, taking place via nucleation, and the nucleation-mediated growth and branching mechanism, the theoretical basis of crystallographic mismatch nucleation that governs fiber branching and formation of three-dimensional fiber networks is presented. In connection to the multi-domain fiber network formation, which is governed by the primary nucleation and the subsequent formation of single fiber networks from nucleation centers, the control of the primary nucleation rate will be considered. Based on the understanding on the the gelation mechanism, the engineering strategies of soft functional materials of this type will be systematically discussed. These include the control of the nucleation and branching-controlled fiber network formation in terms of tuning the thermodynamic driving force of the gelling system and introducing suitable additives, as well as introducing ultrasound. Finally, a summary and the outlook of future research on the basis of the nucleation-growth-controlled fiber network formation are given.