I am waiting for a wire transfer from America but it still hasn’t come through. Do Monzo support this??
Not directly. You’ll need to use something like Transferwise which will give you a proper IBAN number and you can do an instant transfer back to your Monzo.
When I have my details to said company I gave them the IBAN and BIC number. 
It’s hit and miss whether it will work or the funds will return to the sender. As mentioned above Monzo recommend you use Transferwise.
For your Monzo account though? They might work but aren’t officially supported - https://monzo.com/blog/2018/07/24/receiving-international-payments (not sure if there’s a more up to date update than that but I think that one covers it).
A number of things here.
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Monzo do not officially support international bank transfers right now. They have been clear from the start about this. @caspararemi posted the link above.
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International bank transfers to Monzo can ‘sometimes’ work depending on where the money comes from. I can transfer from my Irish bank account to Monzo for example. Unfortunately, it is not known which works well and Monzo are clear it might not work so don’t take the risk right now.
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I believe international bank payments are not direct transfers from Bank A to Bank B. Bank A may need to send it to Bank C, who sends it to Bank D, who sends it to Bank B. Think of it like a daisy chain. Depending how long the chain is, is how long it will take to get to you. Could be a few days, it could be a number of days. Natwest is Monzo’s correspondent bank, for example.