  Quantum coherence has wide-ranging applications from quantum thermodynamics
to quantum metrology, quantum channel discrimination and even quantum biology.
Thus, detecting and quantifying coherence are two fundamental problems in
quantum resource theory. Here, we introduce feasible methods to detect and
estimate the coherence by constructing coherence witnesses for any
finite-dimensional states. Our coherence witnesses detect coherent states by
testing whether the expectation value of the witness is negative or not. Two
typical coherence witnesses are proposed and discussed based on our
witness-constructing method, which are also used to estimate the robustness of
coherence, $l_1$-norm and $l_2$-norm of coherence measures. Furthermore, we
compare one of our coherence witness with a previously introduced witness, by
proving that our witness is strictly stronger than that previous witness. We
also present an application of coherence in a quantum metrology task, in which
we estimate an unknown parameter by measuring our coherence witness.
