  We discuss quadratic gravity where terms quadratic in the curvature tensor
are included in the action. After reviewing the corresponding field equations,
we analyze in detail the physical propagating modes in some specific
backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free.
Then we point out that for flat backgrounds the pure $R^2$ theory propagates
only a scalar massless mode and no spin-two tensor mode. However, the latter
emerges either by expanding the theory around curved backgrounds like de Sitter
or anti-de Sitter, or by changing the long-distance dynamics by introducing the
standard Einstein term. In both cases, the theory is modified in the infrared
and a propagating graviton is recovered. Hence we recognize a subtle interplay
between the UV and IR properties of higher order gravity. We also calculate the
corresponding Newton's law for general quadratic curvature theories. Finally,
we discuss how quadratic actions may be obtained from a fundamental theory like
string- or M-theory. We demonstrate that string theory on non-compact $CY_3$
manifolds, like a line bundle over $\mathbb{CP}^2$, may indeed lead to gravity
dynamics determined by a higher curvature action.
