Many soft materials can be described as network-forming liquids, i.e., as dispersions of particles connected by transient elastic bridges. Their cooperative dynamic behavior exhibits striking features, characterized by non-linearities (shear thinning and thickening), instabilities (shear banding, rheochaos) and heterogeneities, which lack any microscopic understanding. I will introduce in this talk a simplified model of transient-network liquid, composed by particles and bridging polymers, amenable to detailed theoretical, numerical and experimental analysis. Three different phases - sol, gel and coexistence - conform the model phase diagram. The gel phase is stable and broad, allowing a good microscopic characterization of gelation and gel dynamics. As we cross the sol-gel percolation line, a time-scale separation emerges, with a microscopic time scale $t_1$, associated with local particle rearrangements, and a mesoscopic one, $t_2$, controled by the polymer residence time. For times shorter than $t_2$ the transient-network liquid behave as a disordered solid. The dynamics in the gel phase is highly heterogeneous, and resembles that observed in glassy systems and other disordered materials. In particular, the van Hove distribution for particle displacements is strongly non-gaussian, with a bimodal structure due to the coexistence of arrested and mobile particles in the gel. The simplicity of the model allows us to propose a simple mathematical description that captures the observed dynamic heterogeneities, also providing more general insights into the origin of dynamic heterogeneity in disordered materials.