invalid use of incomplete type

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The reason is that when instantiating a class template, all its declarations (not the definitions) of its member functions are instantiated too. The class template is instantiated precisely when the full definition of a specialization is required. That is the case when it is used as a base class for example, as in your case.

So what happens is that A<B> is instantiated at 

class B : public A<B>

at which point B is not a complete type yet (it is after the closing brace of the class definition). However, A<B>::action‘s declaration requires B to be complete, because it is crawling in the scope of it:

Subclass::mytype

What you need to do is delaying the instantiation to some point at which B is complete. One way of doing this is to modify the declaration of action to make it a member template.

template<typename T>
void action(T var) {
    (static_cast<Subclass*>(this))->do_action(var);
}

It is still type-safe because if var is not of the right type, passing var to do_action will fail.

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