Backup and restore: cheapest, and recovery takes hours.
Warm standby: a small copy runs in another region and is scaled up when needed. Recovery takes minutes.
Hot standby (active-passive): a full second region, fed by replication, receives no users until failover. Recovery takes seconds to minutes.
Active-active: both regions serve users all the time. Fastest to recover and best for latency, but hardest: two regions accepting writes must agree, so most designs give each dataset one home region, or accept conflict-resolution rules.

Traffic is steered by DNS with health checks (a low TTL speeds failover, but some clients cache anyway) or by a global load balancer. Cross-region copies lag by tens to hundreds of milliseconds, so expect to lose the last moments of writes in a sudden failover. Some laws also require certain user data to stay in specific countries, which affects where copies may live.

When a whole region goes dark