Abstract: Link prediction is a significant and challenging task in network science, which plays an important role in friend recommendations, the discovery of biological interactions, link navigation, and product recommendations. Since the rise of link prediction, many methods have been proposed. Due to the simplicity, interpretability, high efficiency, scalability, and satisfactory performance, local similarity indices are widely used in various research fields and applications. Under the 2-hop-based neighborhood analytical framework, most of the indices are proposed based on the network organization mechanisms including homophily, clustering and triadic closure. In the last decade, the emergence of local community paradigm, Hebb theory and new arguments about the rationality of the 2-hop-based framework has greatly promoted the development of local similarity indices. This paper aims at sorting out and discussing these new findings.