Link prediction in complex networks has gained significant attention from both physical and computer science communities. This article reviews recent advancements in link prediction algorithms, emphasizing physical perspectives and approaches such as random-walk-based methods and maximum likelihood methods. It also introduces three typical applications: network reconstruction, evaluation of network evolution mechanisms, and classification of partially labeled networks. Finally, it outlines future challenges in link prediction algorithms. The article is organized into several sections. The first section provides an introduction to link prediction, explaining its importance in various fields and the challenges it poses. The second section describes the problem and evaluation metrics used to assess the accuracy of prediction algorithms. The third section discusses similarity-based algorithms, which are the simplest framework for link prediction. These algorithms assign scores to pairs of nodes based on their similarity, and the non-observed links are ranked according to these scores. The fourth and fifth sections introduce maximum likelihood algorithms and probabilistic models for link prediction. The sixth section presents applications of link prediction algorithms, including network reconstruction, evaluation of network evolution mechanisms, and classification of partially labeled networks. The final section outlines future challenges in link prediction algorithms.Link prediction in complex networks has gained significant attention from both physical and computer science communities. This article reviews recent advancements in link prediction algorithms, emphasizing physical perspectives and approaches such as random-walk-based methods and maximum likelihood methods. It also introduces three typical applications: network reconstruction, evaluation of network evolution mechanisms, and classification of partially labeled networks. Finally, it outlines future challenges in link prediction algorithms. The article is organized into several sections. The first section provides an introduction to link prediction, explaining its importance in various fields and the challenges it poses. The second section describes the problem and evaluation metrics used to assess the accuracy of prediction algorithms. The third section discusses similarity-based algorithms, which are the simplest framework for link prediction. These algorithms assign scores to pairs of nodes based on their similarity, and the non-observed links are ranked according to these scores. The fourth and fifth sections introduce maximum likelihood algorithms and probabilistic models for link prediction. The sixth section presents applications of link prediction algorithms, including network reconstruction, evaluation of network evolution mechanisms, and classification of partially labeled networks. The final section outlines future challenges in link prediction algorithms.