How are SIP numbers routed at & between Telephony Service Providers

My googlfu has been failing me, and I'd really appreciate it if someone could point me in the right direction.

How are numbers for SIP really routed? And what I mean by this is, how is it learnt that 01234567890@mytelcom.com is learnt to be with my Telephony provider? If I am calling from Verizon UK, how do they know where to send that call?

I feel like I've missed the boat here a little as I worked at an ISP for a while, that was a SIP provider, & never took enough interest in it other than "we send the calls to Gamma, or BT's IP Exchange". But surely there are tables or similar that are updated that allow resolution of a number to a domain? I really don't know. And I do have recollections of problems with calls from specific providers, such as Vodafone, and reaching our lines sometimes; as in you can call from all providers except Vodafone. This was always something that was passed up to the upstream SP such as Gamma and BT to resolve. My understanding of the resolution was always that this was not an outage, or fault as such, more a mismanagement by someone in the chain.

If someone can point me at some recommended reading, or give a simple overview that would be appreciated.