Can a class member function template be virtual?

I have heard that C++ class member function templates can't be virtual. Is this true?

If they can be virtual, what is an example of a scenario in which one would use such a function?

Templates are all about the compiler generating code at compile-time. Virtual functions are all about the run-time system figuring out which function to call at run-time.

Once the run-time system figured out it would need to call a templatized virtual function, compilation is all done and the compiler cannot generate the appropriate instance anymore. Therefore you cannot have virtual member function templates.

However, there are a few powerful and interesting techniques stemming from combining polymorphism and templates, notably so-called type erasure.

From C++ Templates The Complete Guide:

Member function templates cannot be declared virtual. This constraint is imposed because the usual implementation of the virtual function call mechanism uses a fixed-size table with one entry per virtual function. However, the number of instantiations of a member function template is not fixed until the entire program has been translated. Hence, supporting virtual member function templates would require support for a whole new kind of mechanism in C++ compilers and linkers. In contrast, the ordinary members of class templates can be virtual because their number is fixed when a class is instantiated

C++ doesn't allow virtual template member functions right now. The most likely reason is the complexity of implementing it. Rajendra gives good reason why it can't be done right now but it could be possible with reasonable changes of the standard. Especially working out how many instantiations of a templated function actually exist and building up the vtable seems difficult if you consider the place of the virtual function call. Standards people just have a lot of other things to do right now and C++1x is a lot of work for the compiler writers as well.

When would you need a templated member function? I once came across such a situation where I tried to refactor a hierarchy with a pure virtual base class. It was a poor style for implementing different strategies. I wanted to change the argument of one of the virtual functions to a numeric type and instead of overloading the member function and override every overload in all sub-classes I tried to use virtual template functions (and had to find out they don't exist.)