I know that OLAP is used in Power Pivot, as far as I know, to speed up interacting with data.
But I know that big data databases like Google BigQuery and Amazon RedShift have appeared in the last few years. Do SQL targeted BI solutions like Looker and Chart.io use OLAPs or do they rely on the speed of the databases?
Looker relies on the speed of the database but does model the data to help with speed. Mode and Periscope are similar to this. Not sure about Chartio.
OLAP was used to organize data to help with query speeds. While used by many BI products like Power Pivot and Pentaho, several companies have built their own ways of organizing data to help with query speed. Sometimes this includes storing data in their own data structures to organize the data. Many cloud BI companies like Birst, Domo and Gooddata do this.
Looker created a modeling language called LookML to model data stored in a data store. As databases are now faster than they were when OLAP was created, Looker took the approach of connecting directly to the data store (Redshift, BigQuery, Snowflake, MySQL, etc) to query the data. The LookML model allows the user to interface with the data and then run the query to get results in a table or visualization.