Supersolidity is a highly counterintuitive phenomenon in which a system spontaneously breaks translational symmetry, resembling a solid, while maintaining the frictionless flow of a superfluid. While the concept of supersolidity has been extensively studied and debated in the context of helium, ultracold atoms have emerged as a promising alternative platform. In this presentation, I will discuss the physical mechanisms underlying the formation of the supersolid state in a trapped Bose-Einstein condensate of magnetic atoms. I will then describe the collective excitation spectra across the superfluid-supersolid phase transition, where Higgs-like amplitude excitations coexist with sound modes. I will also explain how a supersolid in a toroidal geometry can serve as an ideal platform for the clean study of Higgs-like modes. In particular, I will show how this geometry gives rise to isolated Higgs modes and, subsequently, massive Higgs quasiparticles. Finally, I will discuss rotation-driven supersolidity and the emergence of re-entrant phases arising from the interplay between vortex and crystalline order in a supersolid