  The paper reassesses the old but still controversial problem of the
transverse force on a vortex and the vortex mass. The transverse force from
free bulk quasiparticles on the vortex, both in the Bose and the Fermi liquid,
originates from the Aharonov--Bohm effect. However, in the Fermi liquid one
should take into account peculiarities of the Aharonov--Bohm effect for BCS
quasiparticles described by two-component spinor wave functions. There is no
connection between the transverse force (either from free bulk quasiparticles
or from vortex-core bound quasiparticles) and the spectral flow in the vortex
core in superfluid Fermi liquid, in contrast to widely known claims. In fact,
there is no steady spectral flow in the core of the moving vortex, and the
analogy with the Andreev bound states in the SNS junction, where the spectral
flow is really possible, is not valid in this respect.
  The role of the backflow on the vortex mass is clarified. The backflow is an
inevitable consequence of a mismatch between the currents inside and outside
the vortex core and restores the conservation of the particle number (charge)
violated by this mismatch. In the Fermi liquid the backflow compensates the
current through the core bound states, which is a source of the vortex mass
(the Kopnin mass). This results in renormalization of the Kopnin vortex mass by
a numerical factor.
