  The Higgs bosons and the top quark decay into rich and diverse final states,
containing both light and heavy quarks, gluons, photons as well as W and Z
bosons. This article reviews the challenges involved in reconstructing Higgs
and top events at the FCC-ee and identifies the areas where novel developments
are needed. The precise identification and reconstruction of these final states
at the FCC-ee rely on the capability of the detector to provide excellent
flavour tagging, jet energy and angular resolution, and global kinematic event
reconstruction. Excellent flavour tagging performance requires low-material
vertex and tracking detectors, and advanced machine learning techniques as
successfully employed in LHC experiments. In addition, the Z pole run will
provide abundant samples of heavy flavour partons that can be used for
calibration of the tagging algorithms. For the reconstruction of jets, leptons,
and missing energy, particle-flow algorithms are crucial to explore the full
potential of the highly granular tracking and calorimeter systems, and give
access to excellent energy-momentum resolution and precise identification of
heavy bosons in their hadronic decays. This enables, among many other key
elements, the reconstruction of Higgsstrahlung processes with leptonically and
hadronically decaying Z bosons, and an almost background-free identification of
top quark pair events. Exploiting the full available kinematic constraints
together with exclusive jet clustering algorithms will allow for the
optimisation of global event reconstruction with kinematic fitting techniques.
