Dynamic models and statistical inference for the diffusion of information in social networks is an area which has witnessed remarkable progress in the last decade due to the proliferation of social networks. Modeling and inference of diffusion of information has applications in targeted advertising and marketing, forecasting elections, predicting investor sentiment and identifying epidemic outbreaks. This chapter discusses three important aspects related to information diffusion in social networks: (i) How does observation bias named friendship paradox (a graph theoretic consequence) and monophilic contagion (influence of friends of friends) affect information diffusion dynamics. (ii) How can social networks adapt their structural connectivity depending on the state of information diffusion. (iii) How one can estimate the state of the network induced by information diffusion. The motivation for all three topics considered in this chapter stems from recent findings in network science and social sensing. Further, several directions for future research that arise from these topics are also discussed.