Online social networks are constantly growing in popularity. They enable users to interact with one another and shifting their relations to the virtual world. Users utilize social media platforms as a mean for a rich variety of activities. Indeed, users are able to express their opinions, share experiences, react to other users' views and exchange ideas. Such online human interactions take place within a dynamic hierarchy where we can observe and distinguish many qualities related to relations between users, concerning influential, trusted or popular individuals. In particular, influence within Social Networks (SN) has been a recent focus in the literature. Many domains, such as recommender systems or Social Network Analysis (SNA), measure and exploit users’ influence. Therefore, models discovering and estimating influence are important for current research and are useful in various disciplines, such as marketing, political and social campaigns, recommendations and others. Interestingly, interactions between users can not only indicate influence but also involve trust, popularity or reputation of users. However, all these notions are still vaguely defined and not meeting the consensus in the SNA community. Defining, distinguishing and measuring the strength of those relations between the users are also posing numerous challenges, on theoretical and practical ground, and are yet to be explored. Modelization of influence poses multiple challenges. In particular, current state-of-the-art methods of influence discovery and evaluation still do not fully explore users’ actions of various types, and are not adaptive enough for using different SN. Furthermore, adopting the time aspect into influence model is important, challenging and in need of further examination part of the research. Finally, exploring possible connections and links between coinciding notions, like influence and reputation, remains to be performed.In this thesis, we focus on the qualities of users connected to four important concepts: influence, reputation, trust, and popularity, in the scope of SNA for influence modeling. We analyze existing works utilizing these notions and we compare and contrast their interpretations. Consequently, we emphasize the most important features that these concepts should include and we make a comparative analysis of them. Accordingly, we present a global classification of the notions concerning their abstract level and distinction of the terms from one another, which is a first and required contribution of the thesis. Consequently, we then propose a theoretical model of influence and present influence-related ontology. We also present a distinction of notion not yet explored in SNA discipline -- micro-influence, which targets new phenomena of users with a small but highly involved audience, who are observed to be still highly impactful. Basing on the definitions of the concepts, we propose a practical model, called Action-Reaction Influence Model (ARIM). This model considers type, quality, quantity, and frequency of actions performed by users in SN, and is adaptive to different SN types. We also focus on the quantification of influence over time and representation of influence causal effect. In order to do that, we focus on a particular SN with a specific characteristic - citation network. Indeed, citation networks are particularly time sensitive. Accordingly, we propose Time Dependent Influence Estimation (TiDIE), a model for determining influence during a particular time period between communities within time-dependent citation networks. Finally, we also combine two of the abovementioned notions, influence and reputation, in order to investigate the dependencies between them. In particular, we propose a transition method, ReTiDIE, that uses influence for predicting the reputation. For each of the proposed approaches, experiments have been conducted on real-world datasets and demonstrate the suitability of the methods