You, like me, probably downloaded the new Messages Beta the second you found out that it was available. It seemed like something that Apple should have released months ago. The problem that you, like me, may be facing is how you actually get your conversations to sync across all your devices, and how you can see those conversations on your Mac.
First, take a quick step back. There are two ways you can send an iMessage. To an iPhone phone number, or to an email address (same thing with FaceTime, by the way). iPads, iPod touchs, and now the Mac all can only use email addresses as, logically, they have no phone number.
And therein lies the problem. Because your Mac can only be reached through an email address, any iMessage conversation that is being sent to your iPhone's number won't be seen by Messages on your Mac.
There is a somewhat roundabout solution to this problem, though. On your iPhone, open up Settings —> Messages —> Receive At and make sure that you log in with your Apple ID (at the top) and that your email address (along with your phone number) is shown as an option to be reached at (you can add as many other emails as you'd like, too). Now, and here is the key, change your Caller ID (at the bottom) to your email address. This way, when you iMessage someone, it will come from your email address and will thus be available on your Mac in Messages as well.
There are a few catches, however. For one, if someone initiates the conversation by iMessaging to your phone number, that particular message will not be seen in Messages on your Mac. But, when you reply — because you have your Caller ID set to your email address — you will automatically make any further replies to that conversation sent to your email address. The other catch, of course, is that even with this setup correctly, should you ever have to fall back on SMS for a message or two, those particular messages will not show up in Messages on your Mac.
A thank you to @mattgibstein for help in clarifying some of the finer points in this post.