  Since the B-mode polarization of the cosmic microwave background (CMB) was
detected by the BICEP2 experiment and an unexpectedly large tensor-to-scalar
ratio, $r=0.20^{+0.07}_{-0.05}$, was found, the base standard cosmology should
at least be extended to the 7-parameter $\Lambda$CDM+$r$ model. In this paper,
we consider the extensions to this base $\Lambda$CDM+$r$ model by including
additional base parameters relevant to neutrinos and/or other neutrino-like
relativistic components. Four neutrino cosmological models are considered,
i.e., the $\Lambda$CDM+$r$+$\sum m_\nu$, $\Lambda$CDM+$r$+$N_{\rm eff}$,
$\Lambda$CDM+$r$+$\sum m_\nu$+$N_{\rm eff}$, and $\Lambda$CDM+$r$+$N_{\rm
eff}$+$m_{\nu,{\rm sterile}}^{\rm eff}$ models. We combine the current data,
including the Planck temperature data, the WMAP 9-year polarization data, the
baryon acoustic oscillation data, the Hubble constant direct measurement data,
the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data,
the cosmic shear data, and the BICEP2 polarization data, to constrain these
neutrino cosmological models. We focus on the constraints on the parameters
$\sum m_\nu$, $N_{\rm eff}$, and $m_{\nu,{\rm sterile}}^{\rm eff}$. We also
discuss whether the tension on $r$ between Planck and BICEP2 can be relieved in
these neutrino cosmological models.
