In the context of dualities for supersymmetric theories, mirror symmetry plays a crucial role. Recently, an algorithm to dualize a theory into its mirror dual has been developed, both for 3d N = 4 linear quivers and for their 4d N = 1 uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the 3d theories, where mirror symmetry is realized as S-duality, but it is entirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of S-duality on the quiver. In this thesis we use this tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. In particular, the 4d index/3d partition function of a bad theory is given by a sum of terms each involving a Dirac delta distribution, enforcing a particular constraint on the fugacities/FI parameters, which multiplies the 4d index/3d partition function of an interacting good SCFT and various singlets. At first, we focus on the bad SQCD, with USp(2Nc) gauge group in 4d and U(Nc) gauge group in 3d. The resulting 4d index/3d partition function identity is then used locally on linear quivers of the same kind and with many bad nodes.