How to make iPhone texts and iMessages appear across all your Apple devices
One of the advantages of Apple's iMessage system is the ability to see and respond to iPhone texts across multiple Apple devices. AppleInsider shows you how to set up the feature and get messaging on your iPad, Mac and more.

Go into the Settings app on your iPhone, then scroll down until you find Messages. Assuming iMessage is on -- which it presumably will be -- the next step is to go into Text Message Forwarding.

Here you should see compatible devices signed into the same Apple ID, and you can toggle them on and off at will. This includes Macs and iPads, which of course don't normally handle SMS messages.
Next, go back up a level in Messages, then select Send & Receive. Be sure to set your phone number as both an origin and destination, rather than just an email address. You may have to add an email address to "You can be reached by iMessage at" in order to see "Start new conversations from" appear.

If you have an iPad, find the same Send & Receive menu within the Settings app, and make sure the information matches what was selected on your iPhone.
Mac owners should launch the Messages app itself, open up Preferences, and hit the Accounts tab. As long as you're signed into the proper Apple ID, the only thing needed here is to once again make sure origins and destinations are the same as above.

Be warned that while you might like the idea of receiving texts across multiple devices, there are potential problems.
On a basic level, if all of your devices are in the same room or house, several simultaneous notifications can create a cacophony. You might also prefer answering on a specific device, and/or want others to be distraction-free. Then there's the matter of privacy, since an iPad sitting on the couch might expose an otherwise private iPhone conversation.

Go into the Settings app on your iPhone, then scroll down until you find Messages. Assuming iMessage is on -- which it presumably will be -- the next step is to go into Text Message Forwarding.

Here you should see compatible devices signed into the same Apple ID, and you can toggle them on and off at will. This includes Macs and iPads, which of course don't normally handle SMS messages.
Next, go back up a level in Messages, then select Send & Receive. Be sure to set your phone number as both an origin and destination, rather than just an email address. You may have to add an email address to "You can be reached by iMessage at" in order to see "Start new conversations from" appear.

If you have an iPad, find the same Send & Receive menu within the Settings app, and make sure the information matches what was selected on your iPhone.
Mac owners should launch the Messages app itself, open up Preferences, and hit the Accounts tab. As long as you're signed into the proper Apple ID, the only thing needed here is to once again make sure origins and destinations are the same as above.

Be warned that while you might like the idea of receiving texts across multiple devices, there are potential problems.
On a basic level, if all of your devices are in the same room or house, several simultaneous notifications can create a cacophony. You might also prefer answering on a specific device, and/or want others to be distraction-free. Then there's the matter of privacy, since an iPad sitting on the couch might expose an otherwise private iPhone conversation.
Comments
I use iCloud's aliases to sort out which specific device gets and sends what. Use only a specific email alias per device, and add it to my address book with the device name.
I have setup forwarding so that my iPhone will receive most of the texts/messages/chats/calls/FaceTimes/etc, as well as the specific device it was send to, except for my better-half's, that is.
BTW, I have been an iTools/.Mac/MobileMe/iCloud user since the beginning, and have created several aliases back then, which it seems that you cannot create as many anymore now.
iPhone 6s.
Reboot the phone.
If that doesn't work, log out of iCloud and log back in.
Other devices may need to be logged in iCloud in order to make Text Message Forwarding appear. If there is no other device logged in to iCloud Text Message Forwarding may not appear, I guess.
Obviously it wasn't syncing because it wasn't plugged in but it so annoying I just decided it wasn't worth the hassle anymore. It would totally interrupt what you were doing and you had to attend to the pop up for it to go away.
UPDATE: I say that, and now I can't log in to iMessage on my Mac at home...
I have a question.
If I am communicating on a text thread with my family from my iPhone, and two are android users, and one is an iPhone user, can the iPhone user pull up our group text message on another device when his data plan is connected to his iPhone?