While the Internet is a network infrastructure compromised of several routers, hubs, gateways, switches the hardware is incredibly different then what we use. An example of a carrier-grade router below (Cisco CRS-1, Juniper MX960):
Some of these devices can route millions of packets per second and commonly have optical interfaces up through but not limited to OC-768 (~40 Gbps). These machines use certain protocols such as Border Gateway Protocol (BGP), Open Shortest First Path (OSPF) and/or Intermediate System-to-Intermediate System (IS-IS, yes it is still in use today) to exchange routing information between networks and varying locations. BGP is the protocol responsible for the maintaining the majority of routing on the Internet. These routers are typically interconnected through fiber optic line laid through cities, country sides, etc.
Just like any local network but on a larger geographical scale, ISPs also have backbone and access layer (PE or Provider Edge) implementations. If you order a circuit or internet connection, the cabling from your location and WAN-facing interface typically makes it back to an interface on one of these devices. For a provider, it is common to 'multiplex' (mux) enterprise grade connections into a single interface. For example, a provider can break a T3/DS3 interface (44.736 Mbit) into 28 separate T1/DS1 (1.544 Mbit) for multiple various customers.
While these devices have implemented their own complexities, they still use the same TCP/IP protocol suite that your router at home uses to transmit and receive data.