  We first analyze the recent experimental data on the nuclear spin-lattice
relaxation rate of the Weyl semimetal TaP. We argue that its non-monotonic
temperature dependence is explained by the temperature dependent chemical
potential of Weyl fermions. We also develop the theory of the Knight shift in
Weyl semimetals, which contains two counteracting terms. The diamagnetic term
follows $-\ln[W/\max(|\mu|,k_BT)]$ with $W$, $\mu$ and $T$ being the high
energy cutoff, chemical potential and temperature, respectively, and is always
negative. The paramagnetic term scales with $\mu$ and changes sign depending on
the doping level. Altogether, the Knight shift is predicted to vanish or even
change sign upon changing the doping or the temperature, making it a sensitive
tool to identify Weyl points. We also calculate the Korringa relation for Weyl
semimetals which shows an unusual energy dependence rather than being constant
as expected for a non-interacting Fermi system.
