What determines differences in wealth accumulation across households? We document two new empirical facts on this old question. First, the variation in wealth accumulation by income is mainly driven by differences in asset market participation rather than differences in the invested amounts, so wealth differences by income are a question of to have or not to have. Second, there are large differences by income in opportunities for asset market participation, so market incompleteness is income-dependent. We develop a novel model of wealth accumulation with a focus on asset market participation and income-dependent market incompleteness. We show that the calibrated model closely accounts for the differences in wealth accumulation across households and the joint distribution of income and wealth. We find the income dependence market incompleteness is a key driver of differences in wealth accumulation. Finally, we show that a policy facilitating access to the housing market improves wealth accumulation, albeit mostly for the middle class.