What is template metaprogramming in C++ and what are its applications?

Template metaprogramming (TMP) performs computation at compile time using templates. Templates are Turing-complete - can compute anything. Techniques: recursive template instantiation, template specialization, SFINAE (substitution failure is not an error), constexpr (C++11+), if constexpr (C++17). Applications: type traits (std::is_integral), compile-time assertions, loop unrolling, expression templates (Eigen), policy-based design. Benefits: zero runtime overhead, type-safe. Drawbacks: complex syntax, long compile times, cryptic errors. Modern C++ (concepts, constexpr) simplifies many TMP use cases.