Confused about NAT and CONNTRACK!

I'm working with iptables and I find myself a little confused about NAT, so I would like to make a couple of questions.

1. Does the router NAT the same way my pc does, with NAT rules? If not what's the difference?
2. If they are affected at all, how are the conntrack entries affected in my pc if the NAT is done by the router and not my pc?
3. If the SNAT (Source NAT) changes the "dst" field in the conntrack entries reply part and substitutes it with that of my gateway, how does DNAT affects conntrack entries in my pc?

To be more clear, I want to have a deep detailed understanding of the NAT and Conntrack Module, and how they work together. If you have any article related to that, it would be very helpful.