The newest buzz word on the block is Lean UX. Lean UX is basically doing UX in the context of Agile development. It's a faster more iterative approach to web design.
Where does research fit into a lean process?
A great approach is The The Design Sprint which is a 5 day process that aims to speed up the process of building a product.
The design sprint is great for a minimal viable product but is harder to implement on established products. I have used the resources for idea generation but the majority of UX research is usually done prior to the sprint.
It's hard to convince companies to go the Lean UX route unless the team is very small and I have yet to see user research fit neatly inside a lean process unless it was desk or guerilla research.
An excellent book on this topic is Lean UX. Buy it, it just may help you to get your company onboard.