In this thesis we contribute to the understanding of online social networks, temporal networks, and non-equilibrium dynamics.
As the title of this work suggests, this thesis is split into two parts, \emph{monitoring} and \emph{modelling} social networks.
In the first half we look at current methods for understanding the behaviour and influence of individual users within a social network, and assess their robustness and effectiveness.
In particular, we look at the role that the temporal dimension plays on these methods and the various representations that temporal networks can take.
We introduce a new temporal network representation which describes a temporal network in terms of node behaviour which we use to characterise individuals and collectives.
The new representation is illustrated with examples from the online social network Twitter.
We model two particular aspects of social networks in the second half of this thesis.
The first model, a generalisation of the popular Voter model, considers the dynamics of two opposite opinions in a heterogeneous society which differ by the resolve of their opinion.
The second model investigates how the presence of `anti-bandwagon' agents can prevent the spread of ideas and innovations on a social network, particularly on networks with restrictive topologies.
This contribution offers new ways to analyse temporal networks and online social media, and also provokes new and interesting questions for future research in the field.
