Lots and lots of SQL (a very good thing IMO). This can come in the form of Oracle, Redshift, or any of the commonly available RDS databases (probably not SQL Server though). This is augmented with a lot of Big Data stuff, which used to be pretty diverse (Pig, Hive, raw Hadoop, etc.) but is moving very quickly towards a Spark-centric platform. There is occasionally some commercial software like Tableau/Microstrategy. Apart from that, it is a whole lot of homegrown technology.
As far as architecture is concerned, every team is different. At least on the retail side, we tend to center around a large data warehouse that is currently transitioning from oracle to redshift, and with daily log parsing ETL jobs from most services to populate tables in that data warehouse. Downstream of the data warehouse is fair game for pretty much anything.