Here is how Tealium builds on top itself as your use cases mature.
Data flows from the website through the Data Layer, managed by your Tealium IQ configuration. Everything is within the browser 100%.
Using our Tealium Collect tag, this full Data Layer is passed through to AudienceStream where we can take real-time Enrichment, Segmentation and Action.
The data can also flow through to Data Access which offers a number of options for Event and Audience data in semi-structured or ETL'd format. You can use this to query against with more robust Analytics and BI tools.