  Electron captures by atomic nuclei in dense matter are among the most
important processes governing the late evolution of stars, limiting in
particular the stability of white dwarfs. Despite considerable progress in the
determination of the equation of state of dense Coulomb plasmas, the threshold
electron Fermi energies are still generally estimated from the corresponding
$Q$ values in vacuum. Moreover, most studies have focused on nonmagnetized
matter. However, some white dwarfs are endowed with magnetic fields reaching
$10^9$ G. Even more extreme magnetic fields might exist in super Chandrasekhar
white dwarfs, the progenitors of overluminous type Ia supernovae like SN 2006gz
and SN 2009dc. The roles of the dense stellar medium and magnetic fields on the
onset of electron captures and on the structure of white dwarfs are briefly
reviewed. New analytical formulas are derived to evaluate the threshold density
for the onset of electron captures for arbitrary magnetic fields. Their
influence on the structure of white dwarfs is illustrated by simple analytical
formulas and numerical calculations.
