  We derive novel constraints on millicharged dark matter and ultralight
axion-like particles using pulsar timing and fast radio burst observations.
Millicharged dark matter affects the dispersion measure of the time of arrival
of radio pulses in a way analogous to free electrons. Light pseudo-scalar dark
matter, on the other hand, causes the polarization angle of radio signals to
oscillate. We show that current and future data can set strong constraints in
both cases. For dark matter particles of charge $\epsilon e$, these constraints
are ${\epsilon}/{m_{\rm milli}} \lesssim 10^{-8}{\rm eV}^{-1}$, for masses
$m_{\rm milli}\gtrsim 10^{-6}\,$eV. For axion-like particles, the analysis of
signals from pulsars yields constraints in the axial coupling of the order of
$g/m_a\lesssim 10^{-13} {\rm GeV}^{-1}/(10^{-22}{\rm eV})$. Both bounds scale
as $(\rho/\rho_{\rm dm})^{1/2}$ if the energy density $\rho$ of the components
is a fraction of the total dark matter energy density $\rho_{\rm dm}$. We do a
detailed study of both effects using data from two samples of pulsars in the
galaxy and in globular clusters, as well as data from FRB 121102 and PSR
J0437$-$4715. We show that in both cases actual pulsar data constrain a new
region of the parameter space for these models, and will improve with future
pulsar-timing observations.
