We reviewed the polarization properties of hydrogen lines in the presence of electric and magnetic fields. We first considered the case of completely depolarized hydrogen atoms. Under this assumption, the hydrogen lines manifest complex polarization signatures due to the combined Stark and Zeeman effect tep{c0 CL93}. One can derive convenient analytic expressions for the 1st and 2nd-order moments of the Stokes profile, which nicely summarize the fundamental properties of hydrogen polarization for both cases of deterministic and micro-turbulent electric and magnetic fields tep{c0 CL94,c0 CL95,c0 Ca97}. In particular, it is demonstrated the ``additivity'' of the Stark and Zeeman effects on such integral properties of the line polarization emitted by a gas of depolarized hydrogen atoms. We then generalized the problem to include the possibility of atomic polarization induced in the hydrogen atoms by anisotropic excitation mechanisms (e.g., in chromospheric and coronal plasmas). The complexity of the problem makes it intractable by analytic means, and one must resort to numerical tools. The results show that, in the presence of atomic polarization, the ``additivity'' of the electric and magnetic effects is lost, and an intricated interplay of the two effects occurs tep{c0 Ca05}. In particular, we considered two hydrogen lines of diagnostic relevance-Lyα and Hα-formed in a magnetized plasma, and demonstrated the modifications of the scattering polarization that are induced by the additional presence of turbulent, electric microfields of various strengths (typically, the normal field strength of the Holtsmark theory, for various electron densities of the plasma). We showed that the additional presence of these electric microfields can significantly enhance the amount of net circular polarization (NCP) of the Hα line for a given magnetic strength, which can be produced by the so-called alignment-to-orientation transfer mechanism tep[e.g.,][]{c0 La82,c0 Ke84,c0 LL04}, even if the electric microfield distribution is perfectly isotropic tep[see Fig. ref{c0 NCP};][]{c0 CM06}. We argued that this mechanism could explain the large levels of NCP that have recently been detected in several quiescent prominences tep{c0 LA05}, and discussed the implications of this study for the diagnostics of magnetic fields in the solar atmosphere using hydrogen lines.