Preferential attachment models were shown to be very effective in predicting such important properties of real-world networks as the power-law degree distribution, small diameter, etc. Such models also have realistic edge distribution. Many different models are based on the idea of preferential attachment. I will speak about a wide class of preferential attachment models, which includes LCD, Buckley–Osthus, Holme–Kim, random Apollonian networks, and many others. The class is defined in terms of constraints that are sufficient for the study of the degree distribution, the clustering coefficient and other important properties.