Used my card a fair amount today. Never needed alternative payment yet but it’s only day 1 of 7.
Chip and PIN works in most places. Contactless is also accepted most places but according to the shopkeepers has a tendency to fail (not sure if it’s still tied to a £30 limit here too? Maybe need to ask a shopkeeper who knows). Mag-stripe and signature is however still the only available form of card holder verification in some places, even in Reykjavik.
UPDATE 10/10/2016
Used an ATM today. The one outside Geysir gift shop. Drawing 2000 Krona (£14.49 at time of withdrawal), I was presented with two options:
- my card be charged 2000 Kr
- my card be charged £14.49 plus a conversion charge of 42p
Obviously I chose option 1. Not all ATMs in the country can be expected to offer those options though. I probably was just lucky to find that one.
As a side note not directly related to using Monzo, I’d advise taking a lot of money. Not sure if this is limited to Iceland, but shops and restaurants along the tourists routes are extremely expensive. Over £20 for a soup with bread and a latte. Also saw a Scandinavian style woolly hat for over £24 
UPDATE 11/10/2016
As a little help with saving money here, my tour guide for today just told us most shops provide a tax receipt (as in the UK), they vary between 11-25% depending on the type of goods being purchased. Interestingly though, you’re eligible to claim that tax back on departure from Keflavik airport, either in Krona or most foreign currencies. I’ll have to try it.