Dina ElBoghdady and I wrote this morning about how Millennials, the largest and most diverse generation in U.S. history, are poised to impact the housing market — if, that is, they'd all finally move out of their parents' homes.

There are a number of reasons to suspect that Millennials may behave differently in the coming years, as homebuyers and heads of their own households, than previous generations. To round up some of those factors, the following data and graphs come from a new report out today on the state of the nation's housing by the Harvard Joint Center for Housing Studies. The report covers a wealth of trends — from who's buying homes, to how we're paying for them, to what it costs today to be a renter — but the prospects of Millennials are a recurring theme.

As with many other trends — their driving preferences, their job prospects, even their politics — we're waiting to see what happens next with this generation as it ages. But here are some clues:

The share of young adults living with their parents is still unusually high right now.

If young adults were living at home in 2013 at the same rates as in 2007, there would be 2.1 million fewer adults in their 20s, and 300,000 in their 30s living with their parents. Put another way: 2.1 million twenty-somethings would have been part of their own households last year if the economy weren't so bad.

Historically, the share of adults living at home plummets sharply after age 24, as that chart shows. This is why we're expecting a windfall of Millennials to soon move out. Already, we're seeing the first stages of that trend, via Trulia:

Once they move out, this cohort is less likely to own a home than in the past.

Homeownership rates for young adults have fallen as median incomes have: