C++ FAQ Celebrating Twenty-One Years of the C++ FAQ!!!
(Click here for a personal note from Marshall Cline.)
Section 35:
35.1 What's the idea behind templates?
35.2 What's the syntax / semantics for a "class template"?
35.3 What's the syntax / semantics for a "function template"?
35.4 How do I explicitly select which version of a function template should get called?
35.5 What is a "parameterized type"?
35.6 What is "genericity"?
35.7 My template function does something special when the template type T is int or std::string; how do I write my template so it uses the special code when T is one of those specific types?
35.8 Huh? Can you provide an example of template specialization that doesn't use foo and bar?
35.9 But most of the code in my template function is the same; is there some way to get the benefits of template specialization without duplicating all that source code?
35.10 All those templates and template specializations must slow down my program, right?
35.11 So templates are overloading, right?
35.12 Why can't I separate the definition of my templates class from its declaration and put it inside a .cpp file?
35.13 How can I avoid linker errors with my template functions? Updated!
35.14 How does the C++ keyword export help with template linker errors? Updated!
35.15 How can I avoid linker errors with my template classes? Updated!
35.16 Why do I get linker errors when I use template friends?
35.17 How can any human hope to understand these overly verbose template-based error messages?
35.18 Why am I getting errors when my template-derived-class uses a nested type it inherits from its template-base-class?
35.19 Why am I getting errors when my template-derived-class uses a member it inherits from its template-base-class?
35.20 Can the previous problem hurt me silently? Is it possible that the compiler will silently generate the wrong code?
35.21 How can I create a container-template that allows my users to supply the type of the underlying container that actually stores the values?
35.22 Follow-up to previous: can I pass in the underlying structure and the element-type separately?
35.23 Related: all those proxies must negatively reflect on the speed of my program. Don't they?
[35.21] How can I create a container-template that allows my users to supply the type of the underlying container that actually stores the values?

First, let's clarify the question: the goal is to create a template Foo<>, but having the template parameter-list include some particular type of std::vector<T> or std::list<T> or some other (possibly non-standard) container to actually store the values.

Here's one way to do that:

template<typename Underlying>
class Foo {
public:
  // typename value_type is the type of the values within a Foo-container
  typedef typename Underlying::value_type  value_type;

  void insert(const typename value_type& x)
  {
     code to insert x into data_
  }

  ...
private:
  Underlying data_;
};

Foo<std::vector<int> > x;
Foo<std::list<double> > y;
If you want to allow your users to provide you with an underlying container that does not necessarily have a value_type typedef (such as some container from a third party), you could provide the value-type explicitly:
template<typename T, typename Underlying>
class Foo {
public:
  // typename value_type is the type of the values within a Foo-container
  typedef T  value_type;

  void insert(const typename value_type& x)
  {
     code to insert x into data_
  }

  ...

private:
  Underlying data_;
};

Foo<int, std::vector<int> > x;
Foo<double, std::list<double> > y;
However you cannot (yet) provide an unspecified template as a template parameter, such as this:
template<typename T, template<typename> class Underlying>   conceptual only; not C++
class Foo {
public:
  ...
private:
  Underlying<T> data_;      conceptual only; not C++
};

Foo<int, std::vector> x;    conceptual only; not C++
Foo<double, std::list> y;   conceptual only; not C++