In many countries it's illegal for shops to either not accept cards or to charge more for card payments (even though they do cost more, more than 5% of the transaction cost in some cases). I think this measure of hiding away the real cost of card transactions was the main driver for increased usage in earlier years.
Interchange fees are capped at 0.2% debit, 0.3% credit. Somewhat higher (~1.2%) for business cards. These caps do not apply to cards issued outside the EEA, nor do they apply to three-party networks such as Amex.
Despite that this displeases the networks, businesses are allowed to elect to only accept a subset of card categories (i.e. they may decide they accept Debit Mastercard only, not Mastercard Credit or business cards). That said, honor all card rules _within_ a given category have been found enforcible (including that e.g. a merchant can't decide they accept Visa Debit, Debit Mastercard and Mastercard Credit but not Visa Credit - Visa are allowed to say "If you accept Visa Debit and Mastercard Credit, you must also accept Visa Credit")
Processors/Terminal providers will add their own margin on top of these, of course (interchange fees are entirely remitted to the card isssuer)