  We introduce a method for computing conformal blocks of operators in
arbitrary Lorentz representations in any spacetime dimension, making it
possible to apply bootstrap techniques to operators with spin. The key idea is
to implement the "shadow formalism" of Ferrara, Gatto, Grillo, and Parisi in a
setting where conformal invariance is manifest. Conformal blocks in
$d$-dimensions can be expressed as integrals over the projective null-cone in
the "embedding space" $\mathbb{R}^{d+1,1}$. Taking care with their analytic
structure, these integrals can be evaluated in great generality, reducing the
computation of conformal blocks to a bookkeeping exercise. To facilitate
calculations in four-dimensional CFTs, we introduce techniques for writing down
conformally-invariant correlators using auxiliary twistor variables, and
demonstrate their use in some simple examples.
