I've got 0.15% interest currently on my savings account with our brick and mortar bank. We're still figuring out where to roll all of that, but it's not staying there.
I'm getting to the point where this savings account is only going to be a short term holding bucket for a month or so worth of funds - basically where we funnel money coming in and then direct it back out to earn better. We've a line of credit of over $20K instantly available from our credit cards (which we do pay off in full every month). I'm seeing that even if we had an emergency, we could charge it, and then pull funds from one of our other accounts (earning MUCH better %) to pay off before the card was due, so that's sort of where we're heading for our emergency fund. (not recommended if you have debt or difficulties controlling your credit card spending. We don't - we use a rewards card for everyday purchases to earn freebies, and have been given a laughably high credit limit considering we've never paid them a penny of interest)
I am not going to invest the EF, rather find a higher yield savings account like the others suggest. If I can get 2-3% and still have access in under a week, that's good enough as we'd technically never need a huge sum instantly, due to the credit card backup.