One of the main unanswered question of modern Physics is "How does gravity behave at small scales?". The aim of this thesis is to illustrate in a comprehensive but accessible way how to look for deviations from Einstein's theory of General Relativity in this regime, looking at the simplest celestial bodies: static and spherically symmetric ones.

With a conservative and bottom-up approach, at smaller scales the first corrections to the action of General Relativity are generally considered to be terms quadratic in the curvature tensors; while these modifications do not cure the...