  Over the past decades, General Relativity and the concordance $\Lambda$CDM
model have been successfully tested using several different astrophysical and
cosmological probes based on large datasets ({\it precision cosmology}).
Despite their successes, some shortcomings emerge due to the fact that General
Relativity should be revised at infrared and ultraviolet limits and to the fact
that the fundamental nature of Dark Matter and Dark Energy is still a puzzle to
be solved. In this perspective, $f(R)$ gravity have been extensively
investigated being the most straightforward way to modify General Relativity
and to overcame some of the above shortcomings. In this paper, we review
various aspects of $f(R)$ gravity at extragalactic and cosmological levels. In
particular, we consider cluster of galaxies, cosmological perturbations, and
N-Body simulations, focusing on those models that satisfy both cosmological and
local gravity constraints. The perspective is that some classes of $f(R)$
models can be consistently constrained by Large Scale Structure.
