The explosive growth of social networks as convenient communication tools has played an increasingly important role in personal communications, marketing, political struggles, diplomacy and some other aspects. The popularity and huge influences attract much attention of the scholars into the social network research. Through statistics of the papers concerning social networks from the most famous international conferences and journals, we conclude the focuses of the social network research are information diffusion and securities. About the researches on information diffusion, there are four main questions including information diffusion model, factors, influence maximization and prediction. About the researches on security of social networks, there are two main questions including security of users and information. In security of users, spammer identification and cascading failures were discussed. The source identification and control strategy were included in security of information. The related papers of the conferences and journals were introduced and the main research results in the above aspects were stated. Then, the problems, challenges and trends of the information diffusion and securities, which will provide a meaningful guidance to the social network research, were obtained.