Abstract: Starting from a short review on some classical spectral estimates, in particular bounds on the spectral data by the corresponding semi- classical phase space volume such as the Li-Yau and the Lieb-Thirring inequalities, I will discuss in this survey talk a number of open problems and conjectures in this area. On the one hand these are classical unresolved conjectures, on the other hand even slight and natural changes of the classical statement of the problem lead to unresolved questions.