How do boost::variant and boost::any work?

If you read the boost::any documentation they provide the source for the idea: http://www.two-sdg.demon.co.uk/curbralan/papers/ValuedConversions.pdf

It's basic information hiding, an essential C++ skill to have. Learn it!

Since the highest voted answer here is totally incorrect, and I have my doubts that people will actually go look at the source to verify that fact, here's a basic implementation of an any like interface that will wrap any type with an f() function and allow it to be called:

struct f_any
{
   f_any() : ptr() {}
   ~f_any() { delete ptr; }
   bool valid() const { return ptr != 0; }
   void f() { assert(ptr); ptr->f(); }

   struct placeholder
   {
     virtual ~placeholder() {}
     virtual void f() const = 0;
   };

   template < typename T >
   struct impl : placeholder
   {
     impl(T const& t) : val(t) {}
     void f() const { val.f(); }
     T val;
    };
   // ptr can now point to the entire family of 
   // struct types generated from impl<T>
   placeholder * ptr;

   template < typename T >
   f_any(T const& t) : ptr(new impl<T>(t)) {}

  // assignment, etc...
};

boost::any does the same basic thing except that f() actually returns typeinfo const& and provides other information access to the any_cast function to work.

The key difference between boost::any and boost::variant is that any can store any type, while variant can store only one of a set of enumerated types. The any type stores a void* pointer to the object, as well as a typeinfo object to remember the underlying type and enforce some degree of type safety. In boost::variant, it computes the maximum sized object, and uses "placement new" to allocate the object within this buffer. It also stores the type or the type index.

Note that if you have Boost installed, you should be able to see the source files in "any.hpp" and "variant.hpp". Just search for "include/boost/variant.hpp" and "include/boost/any.hpp" in "/usr", "/usr/local", and "/opt/local" until you find the installed headers, and you can take a look.

Edit
As has been pointed out in the comments below, there was a slight inaccuracy in my description of boost::any. While it can be implemented using void* (and a templated destroy callback to properly delete the pointer), the actualy implementation uses any<T>::placeholder*, with any<T>::holder<T> as subclasses of any<T>::placeholder for unifying the type.

boost::any just snapshots the typeinfo while the templated constructor runs: it has a pointer to a non-templated base class that provides access to the typeinfo, and the constructor derived a type-specific class satisfying that interface. The same technique can actually be used to capture other common capabilities of a set of types (e.g. streaming, common operators, specific functions), though boost doesn't offer control of this.

boost::variant is conceptually similar to what you've done before, but by not literally using a union and instead taking a manual approach to placement construction/destruction of objects in its buffer (while handling alignment issues explicitly) it works around the restrictions that C++ has re complex types in actual unions.