The recent economic and sociological literature pays a lot of attention to the issue of income inequality and to preferences for the redistribution. This paper discusses various approaches which pretend to explain what shapes perceptions of income inequality and finally affects preferences for the redistribution. If people in a given country perceive the level of income inequality as too high and unacceptable, they may support various redistributive policies and measures. However, this does not always happen. Perceptions of inequality and preferences for redistribution vary across countries as well as across individuals within countries. The paper overviews existing theoretical and empirical studies and provides their synthesis. In its empirical section, the paper tests a few most frequently mentioned hypotheses. For this, it uses large cross-country data sets from the International Social Survey Program (ISSP) and the European Social Survey (ESS) covering 34 and 25 countries, respectively. One of the main findings is that the public attitude towards inequality depends little on the actual level of inequality. What appears to be more important is whether the society provides functioning escalators to individuals for moving up the socio-economic ladder and whether individuals have recently experienced actual upward mobility. What also matters is whether this mobility is considered by public fair and legitimate. This means that is driven by hard work (and is meritocratic) but not by pure luck, or connections, or bribes (is structural). Therefore, the perception of inequality and redistributive demands are largely shaped by dominant views on fairness, social mobility and trust to the state. If individuals see for themselves feasible prospects for advancement and can achieve more in a way they consider fair, they are more likely to tolerate the income inequality and their redistributive claims tend to become weaker. This brings to the forefront the issue of quality of state institutions and institutional environment. The corruption as a measure of the institutional quality emerges a very strong predictor for larger support to redistributive policies.