Does it cost extra to text internationally?

I'm a US citizen but will be spending the next 12 months in Scotland working on my Masters degree. I have a UK SIM card for my cell phone as well as a UK phone number, but several of my friends and family members have been asking about texting and I honestly don't know the answer. I know there are services like Viber or Skype, but in terms of basic texting (specifically on the iPhone, but other phones as well), what would the other person need to do?

TL, DR: Will someone from the US need to unlock their phone and/or pay extra in order to text me on a UK phone number?

YES obviously

A true text message will cost more to SEND (they are always free to receive)
Typically a US to UK/UK to US text will be about $1.00 to $1.50 a text (!)

But iMessage (iPhone to iPhone) will be free [ uses your data not texts ]

now the UK has ONE network that is cheaper…
O2: Pre-Paid/PAYG SIM - has an international SIM (1p/min to call, 2p/text to send to US)
and it does normal 20p/min calls and texts in the UK…
If you have a Post Paid-Contract/PAYM SIM, for £5.00/month you can add 2000 mins and texts (both ways) AND… They will give you an US Call me No (so people in the US can call it 'as normal' and your UK phone rings.

and AT&T has a bundle you buy to add (250) international Mins and UNL texts (as I recall)
https://www.att.com/...html?tab=1
$1,.99 per min and per text ( worse than I remember)

However…
O2 (again), has an app - the TuGo app.
And it puts your UK O2 Phone Number on your phone (even a US iPhone) and lets you call/send txts and calls using your data/internet allowance.
You do have to be in the UK to enable it, but once done… It works 'free' everywhere, so US bars with their Wi-Fi, or 4G data in the US.

NOW special extra case: iPhone to iPhone
iMessage (not SMS texts) uses data…
so they will NOT cost you either…
BLUE bubbles = iMessage (free on Data)
Green bubbles = Text (and will cost)
… The Apple/iphone needs your other iphone friend's number in your Contacts list, and listed as iPhone (not a normal number) and the same for your friend.

So think about getting an O2 contract SIM for 12 months and paying the extra £10.00 for the international call option, with a CALL ME number. (you can move your UK phone No in 2 days if you need to - even if you are abroad - they will tell you it may not happen, but it always has for me)

O2 International Favorites
https://www.o2.co.uk/shop/international/calling-international-numbers
(as US mobiles and Land lines cost the same to call, it is 3000 mins on any US phone, but UK 'call me' mins will be limited, but you can always call them back.

And just adding international 1p/min calls
international Bolt on *United States of America")
http://international.o2.co.uk/internationaltariffs/calling_abroad_from_uk

O2 TuGo App
https://www.o2.co.uk/apps/tu-go