Etiquette is rooted in tradition. Its role is to tell you what's expected of you in a certain situation, based completely on what the people before you have done. But times change, of course, and we need to give etiquette some room to catch up. Case in point: How you should address wedding invitations today is a totally different ball game from when your parents did it 30 years ago.
There's a great resource here from Emily Post for how to address invites in all the traditional ways, but I happen to think that some of the advice is a little outdated for modern lifestyles. So here are a few spots where it might be a smart move to deviate from the old rules when you're addressing invitations:
She's Not "Mrs. His-Name"
This is so old school that we should put it in a museum. I don't know any gal under retirement age that prefers to be addressed as "Mrs. Oscar Isaac" (unless perhaps you actually marry Oscar Isaac and want to brag about it, in which case, carry on). If she's married and if she took his name, a safer way to address an invitation in 2016 is to "Mr. and Mrs. George and Amal Clooney." If you're looking to be a little less formal, "Amal and George Clooney" works, too.
If She Kept Her Maiden Name (or Part of It)...
Use it. And note that a hyphenated or two-word surname is still a different last name. "Mrs. Jenna Dewan Tatum" is not the same as "Mrs. Jenna Tatum." The proper thing to do is to include her full name followed by her husband's full name on the same line, separated by an "and": Mrs. Jenna Dewan Tatum and Mr. Channing Tatum.
The Living-Together (or Not) Gray Area
For a couple who are not married but living together, include their names and honorifics on the same line, with either the person you know better or whoever is alphabetically first in front. For a couple who's not living together but are, by all means, "together," I would still send one invitation addressed to them both, and mail it to either the person I know best or to the one of the pair who I know handles their social calendar, and list that person's name first. It is certainly OK to mention the other by name, not as "and guest," even if you haven't met their significant other. It sucks to be years into a committed relationship and still be your S.O.'s "plus one."
What About LGBT Couples?
Well, the same rules apply. If they share a name (a hybrid or hyphenated name or whatever it may be), the invitation can read "Mr. and Mr. John and Matt Doe-Smith" on the same line. If they're an established couple but they don't share a surname, put both names on the same line with either the person you know better or whoever is alphabetically first in front, separated by an "and."
Is it "Mrs." or "Ms." for Married Lesbians?
Historically, the Mrs. honorific means "I'm the the wife of ______." A woman who keeps her last name after marriage is typically a "Ms.," whether gay or straight. But a lesbian couple who share a name may prefer to use "Mrs." instead to honor their partner. If you know which they use, then use that one. If not, I would say that "Ms." is a safer bet.
But above all else:
Address People How they Prefer to Be Addressed
There's no governing body for weddings that's going to come and audit your invitations to make sure they're all addressed uniformly and according to strict standards. These people are, presumably, your friends and family, so take a little extra care to address each of your guests in whatever way you see fit. Your widowed grandmother may prefer to be "Mrs. John Smith," while your newly married cousin prefers to stick to her maiden name for now (or forever).
Feel free to pipe up in the comments with your own opinions–"proper etiquette" is changing every day and it's good to hear different perspectives.