Way back in my past I used to research formal methods for software engineering. Actually I still do, though now most of my time is actually using formal methods to make better software.
Formal methods are nothing more than a collection of languages and techniques for modifying and reasoning about things (models) written in those languages. Some of these techniques encompass how the process of building a system is made. Herein lies one of the first problems encountered by formal methods practitioners and that is the almost constant challenge from some, such as many in the agile community, that seem to be religiously against any form of modelling.
To those who believe that code is the only deliverable and the only thing that matters, well, C++, C, Fortran, Clojure etc are all formal languages, and you're probably using many of the techniques from formal methods right now as your write your code.
Language such as B, Alloy, Z, VDM etc do is provide a method of expressing a model without worrying about certain, awkward details of their implementation or execution.
Indeed what is happening here is that we have languages and techniques that allow you to concentrate on reasoning and thinking about the problem you are trying to solve without getting bogged down in the details of the final implementation.
If your first worry is the implementation language, or the operating system, or which libraries to use, etc, then you're most certainly not solving the problem.
At Nokia we had some very great successes using formal methods in an agile manner for the development of a semantic web infrastructure for the "Internet of Things". Concentrating on what the system had to do and then later worrying about how it was implemented meant that when it did come to the time we needed to architect the components and decide on specific implementation issues we already knew how the system was going to work, what tests we would need to run and what the expected answers were going to be.
Indeed, many of the tests were little more than checking that the code behaved the same as our earlier models - regression testing if you like.
This resulted in a huge decrease in the time spent in coding and the effective removal of nearly all (logic) bugs before even the beta releases. In fact most of the bugs turned out to by typos.
Furthermore, when it came to updating the software with additional features, instead of blindly bolting on a new use case we could reduce most of the new feature requests down to library or convenience functions over the core functionality rather than complicating the design with those "new" features.
This latter point is very important in that even though there is pressure to constantly add new features (and the Pareto Principle applies here), most new features are really just convenience functions that already exist in the software.
I even remember one system where management demanded so many new features (all specified as their own use cases) that the system actually ended up implementing not only the same feature many times but features to disable the requested feature...
Ultimately formal methods is a discipline of thinking, rather than any technique to develop software. Just as much as Agile is a discipline of development.
To use formal methods does not mean any form of top-down or Waterfall development, it does not mean that one has to use refinement or a language like B or Z or VDM or Alloy etc. Just the simple act of writing a precondition to a function in C, or expressing a simple class diagram in UML, or ER diagram to explain a database schema (SQL or NoSQL) to demonstrate the workings of a system, or to clarify what something mean IS being formal.
The best agile developers I have seen all have formal methods backgrounds. The reasoning is that they already have the discipline and education and the tools to think and reason about their system, even if applied implicitly. Agile depends upon great communication between the developers and the customers and giving those customers exactly what they need in a manner that avoids technical debt (viz. situational awareness).
Whether we like it or not, great software engineering comes from understanding how our craft works at its most fundamental levels - imagine civil engineering without the mathematics of physics (a classic example), or even ballet without an understanding of human movement?
 Ian Oliver Experiences of Formal Methods in 'Conventional' Software and Systems Design. FACS 2007 Christmas Workshop: Formal Methods in Industry. BCS London, UK, 17 December 2007
 Ian Oliver Experiences of Formal Methods in 'Conventional' Software and Systems Design