Vertical scaling is also known as Scale Up [scaling by adding more power CPU , RAM , DISK ,etc]
Horizontal scaling is better known as Sharding [scaling by adding more server]
A few major challenges from Sharding
Celebrity problem : Also known as Hotspot key problem. Example : In Instagram , if we have data of Ronaldo , Lady Gaga , The Rock , Messi , etc in same shard. The shard will be overwhelmed with read operations. To solve this , we would require re-distribute or reallocate data in different shards or increase shards accordingly
Join and aggreation : Once db is sharded across multiple servers , its hard to perform join/aggregation operation across database shards. Common practice is denormalize the database.
6. Split tiers into individual services
7. Monitoring system
It includes logging and metrics system for operations