Server is Nginx. Evaluating HHVM for migration is an ongoing concern, but there's some edge cases we run in to where it does wonky things. That said, within the next ~12 months, I expect we'll be on it.
MariaDB, with query results cached on Memcache. The data we deal with is massively relational, with some very large tables and result outputs, so there's no way around using a tidy RDBMS for us, and consistency is a big thing.
PHP, with a few tiny, high speed libraries for DB connection management and routing. As far as possible everything uses PHP functions that map directly on to underlying language equiv, and we make a lot of use of streaming and generators, which makes memory overhead nicely manageable. When HHVM becomes a thing for us, we'll then start pulling some of this over to Hack.
That's all set up as a bunch of RESTful APIs, which are reasonably HATEOAS in their outputs. Output format is either JSON or HTML, depending on request params.
Front end is a bunch of React bits. We're slowly converting into React, so initially we used HistoryJS to manage URL history, along with React to render stuff. Qwest for XHR handling, and a few little libraries and helper functions (of note: moment.js and numeral.js).
Everything then gets executed on the client. Current roadmap is to build something akin to React router for managing loading of assets and better history management, and to pull the entire front end into a single application. At the moment, it's better thought of as a bunch of distinct SPAs, operating over a common middleware.
Architecturally, the back end services are written MVA, with data going through our own DAL, with RBAC sitting in front of everything. Caching is handled in the DAL, so everything acts as a black box - models don't know where the data came from, adapters don't know where the model got it's data etc...
The front end is written loosely around a Flux style architecture. Data is held in a single area, as are all methods that interface with state. Those parts sit at the top, and pass data as props down to UI components, written to be dumb as to where there data comes from.
IO is mostly via single HTTP requests, but with the option to hook onto ZMQ for real time interaction.
Hope that helps! I'm currently writing some lower level thoughts on React on our blog (https://builtvisible.com/blog/) with some more advanced stuff coming shortly.
Apologies for the various TLAs. If you need anything explaining further, shout.