In this talk, I will introduce recent progress made on certain problems related to local Arthur packets of classical groups. First, I will introduce my joint work with Freydoon Shahidi towards Jiang's conjecture on the wave front sets of representations in local Arthur packets of classical groups, which is a natural generalization of Shahidi's conjecture, confirming the relation between the structure of wave front sets and the local Arthur parameters. Then, I will introduce my joint work with my students Alexander Hazeltine and Chi-Heng Lo on the intersection problem of local Arthur packets for symplectic and split odd special orthogonal groups, with applications to the Enhanced Shahidi's conjecture and the closure relation conjecture.