According to the UUA, a young adult is someone 18-35. (Yes, a little different from the book classification). Now certainly this is a brad age group, and some of the things the 18-35 year olds might be up to might well be more appealing to the 36-45 year olds (or older) and often young adult groups within congregations consider their events age inclusive (which is to say that they are targeted at the core age, but would not exclude others).
I am no longer a young adult by that definition (I am an old adult now,a s far as I can tell) but since I joined a congregation as a young adult, despite it's having a terrible lack of young adult activites (when I first joined they had a group that had been a young adult group, but had apparently not picked up anyone new who still qualified to be referred to as such in some time), it has been a big issue for me.
And I remain convinced that it is part of maintaining a vibrant community, that you can have a great religious education program, a great high school program and then if those high schoolers all graduate and you have nothing to offer them until they are parents you will lose them. Sure, I joined, but not everyone will. And I wasn't raised anything, so I didn't lose my support group of congregants, since I had never had one.
This post here addresses some great things. My church actually has a website (although I am not a huge fan of it's redesign) and a regularly updated Facebook page.
I co-led a workshop on attracting young adults once, and one of the things we said(which is echoed nicely in the linked post) was that you don't have to reinvent your church, but look at ways to use the things your church does well and how you can best use that to attract young adults (and others, the best ideas will attract lots of people).
*My church is technically no longer referred to as such, it is a congregation. While I understand and even agree with the word choice, I do often fall back on the word church for it's ease of use.
h/t to ChaliceChick for the link