The core task of demography is to estimate current and past population, mortality, fertility and migration by age and sex, and to project them into the future. Demography is one of the most successful areas of social science: its outputs are used by governments at all levels, international organizations, researchers and the private sector. Demographic estimation and projection have traditionally been based on deterministic mathematical models and have not been statistical for the most part. However, demography is in the midst of a revolution in both methods and data. The United Nations has moved towards Bayesian probabilistic projections and estimates for all countries, Also, a wealth of new data sources have become available, especially big data such as social media and mobile phone data. I will review some of the basic ideas of demography, and outline statistical developments and challenges.