  In this paper, we systematically investigate the general dark matter-electron
interactions within the framework of effective field theories (EFT). We
consider both the non-relativistic (NR) EFT and the relativistic EFT
descriptions of the interactions with the spin of dark matter (DM) up to one,
i.e., the scalar ($\phi$), fermion ($\chi$), and vector $(X)$ DM scenarios. We
first collect the leading-order NR EFT operators describing the DM-electron
interactions, and construct especially the NR operators for the vector DM case.
Next, we consider all possible leading-order relativistic EFT operators
including those with a photon field and perform the NR reduction to match them
onto the NR EFT. Then we rederive the DM-bound-electron scattering rate within
the NR EFT framework and find that the matrix element squared, which is the key
input that encodes the DM and atomic information, can be compactly decomposed
into three terms. Each term is a product of a DM response function
$(a_{0,1,2})$, which is essentially a factor of Wilson coefficients squared,
and its corresponding generalized atomic response function ($\widetilde
W_{0,1,2}$). Lastly, we employ the electron recoil data from the DM direct
detection experiments (including XENON10, XENON1T, and PandaX-4T) to constrain
all the non-relativistic and relativistic operators in all three DM scenarios.
We set strong bounds on the DM-electron interactions in the sub-GeV region.
Particularly, we find that the latest PandaX-4T S2-only data provide stringent
constraints on dark matter with a mass greater than approximately 20 MeV,
surpassing those from the previous XENON10 and XENON1T experiments.
