  A perturbative description of Large Scale Structure is a cornerstone of our
understanding of the observed distribution of matter in the universe.
Renormalization is an essential and defining step to make this description
physical and predictive. Here we introduce a systematic renormalization
procedure, which neatly associates counterterms to the UV-sensitive diagrams
order by order, as it is commonly done in quantum field theory. As a concrete
example, we renormalize the one-loop power spectrum and bispectrum of both
density and velocity. In addition, we present a series of results that are
valid to all orders in perturbation theory. First, we show that while
systematic renormalization requires temporally non-local counterterms, in
practice one can use an equivalent basis made of local operators. We give an
explicit prescription to generate all counterterms allowed by the symmetries.
Second, we present a formal proof of the well-known general argument that the
contribution of short distance perturbations to large scale density contrast
$\delta$ and momentum density $\mathbf\pi(\mathbf k)$ scale as $k^2$ and $k$,
respectively. Third, we demonstrate that the common practice of introducing
counterterms only in the Euler equation when one is interested in correlators
of $ \delta$ is indeed valid to all orders.
