There will be a charge for using Monzo’s overdrafts which is how they will make their revenue.
I should have been clearer - AFAIK, that’s the only charge you’ll incur for using a Monzo account (with just one other exception) but you’ll only pay if you decide to use an overdraft, it’s essentially paying interest & there won’t be any punitive fees. I’ll leave Monzo to explain the semantics of interest vs overdraft fees, once they’ve finalised how the pricing will work.
The lack of a bank branch network or a legacy technology stack to maintain means that Monzo can cover it’s costs from overdraft revenue alone.
The banks make £120 - £200 per current account & James (from the Monzo team’s) guess is that at least half of that comes from fees.
That’s Starling for you 
they have said that they are planning to launch a marketplace too & overdrafts first though.