  The calculation of physical quantities in certain quantum field theories such
as those of the Argyres-Douglas type is notoriously hard, due to the lack of a
Lagrangian description. Here we tackle this problem following two alternative
approaches. On the one hand, we use localization on the four-sphere to compute
two-correlators and OPE coefficients in Argyres-Douglas superconformal
theories. On the other hand, we use the conformal bootstrap machinery to put
stringent bounds on such coefficients, only relying on the knowledge of central
charge and conformal dimension of the operators. We compare the results
obtained with these two methods and find good agreement for all rank-one cases
and for the rank-two Argyres-Douglas theories (A_1,A_4) and (A_1,A_5), in the
moduli space of pure SU(5) and SU(6) super Yang-Mills. We also apply our
results from localization to obtain bounds on the dimensions of the lightest
neutral unprotected operators of the CFTs.
