At first we were just using Google Analytics and SQL. A couple years into it I deployed Mixpanel, and eventually we built our entire analytics infrastructure from scratch and used Looker to expose it to the rest of the company.
Here's the 30,000 foot view of how that worked:
https://www.kickstarter.com/backing-and-hacking/this-is-the-...
I was at the company for over 6 years and by the time I left, my data team had people working on data science, machine learning, traditional BI, and of course infrastructure.
I wrote about that experience here:
https://medium.com/@fredbenenson/on-to-the-next-2-271-days-3...
Spoiler alert: I'm now at Y Combinator working on data science with their admissions team, so things have come pretty full circle :)