"Pending" nearly always means one of three things, and none of them is a problem with your domain.
A .uk domain (.co.uk, .uk, .org.uk): the transfer completes the moment your old provider changes the IPS tag to PDR-IN. Until they do, we can only wait — chase them, not us. Once the tag changes, the status in your client area can lag behind by a few hours while our system catches up; the domain itself is already working.
A .com, .net or similar: these need the authorisation (EPP) code from your current provider. If the transfer is sitting at pending, the most common cause is that the code was never entered, was mistyped, or the domain is still locked or has privacy switched on. Send us the code on a ticket and we'll submit it for you. Once submitted, the transfer usually completes within hours and never more than five days.
Nothing was actually started at the other end: ordering a transfer with us doesn't tell your old provider anything. For .uk domains they must change the tag; for others they must unlock the domain and give you the code.
Transfers don't take your website or email offline — a transfer changes who manages the domain, not where it points. If it's been more than a couple of days since the tag changed or the code went in, open a ticket with the domain name and we'll check the registry directly.