  We present a novel combination of the excursion-set approach with the peak
theory formalism in Lagrangian space and provide accurate predictions for halo
and void statistics over a wide range of scales. The set-up is based on an
effective moving barrier. Besides deriving the corresponding numerical
multiplicity function, we introduce a new analytical formula reaching the
percent level agreement with the exact numerical solution obtained via Monte
Carlo realizations down to small scales, $\sim 10^{12} h^{-1}\mathrm{M_\odot}$.
In the void case, we derive the dependence of the effective moving barrier on
the void formation threshold, $\delta_{\rm v}$, by comparison against the
Lagrangian void size function measured in the Dark Energy and Massive Neutrinos
Universe simulations. We discuss the mapping from Lagrangian to Eulerian space
for both halos and voids; adopting the spherical symmetry approximation, we
obtain a strong agreement at intermediate and large scales. Finally, using the
effective moving barrier, we derive Lagrangian void density profiles accurately
matching measurements from cosmological simulations, a major achievement
towards using void profiles for precision cosmology with the next generation of
galaxy surveys.
