Networks are central in the modeling and analysis of many large-scale human and technical systems, and they have applications in diverse fields such as computer science, biology, social sciences, and economics. Recently, network mining has been an active area of research. In this thesis, we study several related network-mining problems, from three different perspectives: the modeling and theory perspective, the computational perspective, and the application perspective. In the bulk of this thesis, we focus on network alignment, where the data provides two (or more) partial views of the network, and where the node labels are sometimes ambiguous. Network alignment has applications in social-network reconciliation and de-anonymization, protein-network alignment in biology, and computer vision. In the first part of this thesis, we investigate the feasibility of network alignment with a random-graph model. This random-graph model generates two (or several) correlated networks, and lets the two networks to overlap only partially. For a particular alignment, we define a cost function for structural mismatch. We show that the minimization of the proposed cost function (assuming that we have access to infinite computational power), with high probability, results in an alignment that recovers the set of shared nodes between the two networks, and that also recovers the true matching between the shared nodes. The most scalable network-alignment approaches use ideas from percolation theory, where a matched node-couple infects its neighboring couples that are additional potential matches. In the second part of this thesis, we propose a new percolation-based network-alignment algorithm that can match large networks by using only the network structure and a handful of initially pre-matched node-couples called seed set. We characterize a phase transition in matching performance as a function of the seed-set size. In the third part of this thesis, we consider two important application areas of network mining in biology and public health. The first application area is percolation-based network alignment of protein-protein interaction (PPI) networks in biology. The alignment of biological networks has many uses, such as the detection of conserved biological network motifs, the prediction of protein interactions, and the reconstruction of phylogenetic trees. Network alignment can be used to transfer biological knowledge between species. We introduce a new global pairwise-network alignment algorithm for PPI networks, called PROPER. The PROPER algorithm shows higher accuracy and speed compared to other global network-alignment methods. We also extend PROPER to the global multiple-network alignment problem. We introduce a new algorithm, called MPROPER, for matching multiple networks. Finally, we explore IsoRank, one of the first and most referenced global pairwise-network alignment algorithms. Our second application area is the control of epidemic processes. We develop and model strategies for mitigating an epidemic in a large-scale dynamic contact network. More precisely, we study epidemics of infectious diseases by (i) modeling the spread of epidemics on a network by using many pieces of information about the mobility and behavior of a population; and by (ii) designing personalized behavioral recommendations for individuals, in order to mitigate the effect of epidemics on that network.