Japan is very cash-based. I've never seen Square or the domestic one (Coiny, I think?) in the wild.
Many stores still do not take credit cards.
A lot of convenience stores will take credit cards, most will take Suica cards (mass transit cards pre-loaded with money). Some vending machines will take Suica cards.
Mobile phone payment is kind of a hassle and requires a credit card as well as a phone that supports it (osaifu keitai). Not all phones do.
Cash is still the preferred method of payment online too -- three of the four options are basically cash: bank transfer (done with cash at an ATM or online if you use a bank that supports it), COD, and payment at a convenience store.
Yes spot on - many restaurants, especially the smaller places do not take credit cards. Even a large chain of Convenience Stores (FamilyMart) do not accept credit cards for payment.
(Way off topic) Japan can be quite strange with banking and ATMs as well. Unlike, for example, the UK, your ATM cards usually will only work on the ATMs of your bank or perhaps in some convenience stores.
For example, my Citibank card only works at Citibank ATMs, and 711 convenience stores, but won't work at a MUFG ATM. You also get charged for withdrawing money outside of "office hours" at an ATM, and some ATMs stop working after 2100.
It was a little bit of a shock moving from London where I walked around with 10 pounds in my pocket to Tokyo where withdrawing and walking around with 500 dollars worth of yen seems pretty normal.
Many stores still do not take credit cards.
A lot of convenience stores will take credit cards, most will take Suica cards (mass transit cards pre-loaded with money). Some vending machines will take Suica cards.
Mobile phone payment is kind of a hassle and requires a credit card as well as a phone that supports it (osaifu keitai). Not all phones do.
Cash is still the preferred method of payment online too -- three of the four options are basically cash: bank transfer (done with cash at an ATM or online if you use a bank that supports it), COD, and payment at a convenience store.