Abstract: I explore the consequence of generalized symmetries in four-dimensional N=1 superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the ABJ anomaly, we find that many of these theories have mixed zero-form/one-form 't Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. I will also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, I highlight a new duality between the diagonal gauging of two D3(SU(N)) theories and SU(N) gauge theory with two adjoints. I conclude with some comments on non-supersymmetric deformations of our work. Event recording: