Following are some of the videos I could gather which presents talks on API design & development.
- How to Design a Good API and Why it Matters?: A great video by Joshua Bloch done some 6 years back. Great one for those looking to understand what API design & development look like and how to get started?
- How to Design Good APIs: This video focus on some of the key aspects such as intuitiveness, documentation of API.
- Life of a Google API Developer: This video presents different aspect of API development.