  Over the last decade, warm dark matter (WDM) has been repeatedly proposed as
an alternative scenario to the standard cold dark matter (CDM) one, potentially
resolving several disagreements between the CDM model and observations on small
scales. Here, we reconsider the most important CDM small-scale discrepancies in
the light of recent observational constraints on WDM. As a result, we find that
a conventional thermal (or thermal-like) WDM cosmology with a particle mass in
agreement with Lyman-$\alpha$ is nearly indistinguishable from CDM on the
relevant scales and therefore fails to alleviate any of the small-scale
problems. The reason for this failure is that the power spectrum of
conventional WDM falls off too rapidly. To maintain WDM as a significantly
different alternative to CDM, more evolved production mechanisms leading to
multiple dark matter components or a gradually decreasing small-scale power
spectrum have to be considered.
