This chapter explores the intricate connections between hoops and a diverse range of related algebraic structures, demonstrating their fundamental role in algebraic logic. We investigate the relationships between hoops and residuated lattices, MTL-algebras, BL-algebras, MV-algebras, product algebras, \(R\ell \) -monoids, BCK-algebras, Wajsberg algebras, Heyting and Hertz algebras, lattice implication algebras, Hilbert algebras, and L-algebras. Specifically, we establish key equivalences: Bounded \(\vee \) -hoops are equivalent to divisible residuated lattices. Bounded basic hoops are equivalent to BL-algebras. Bounded Wajsberg hoops are equivalent to both MV-algebras and Wajsberg algebras. Product algebras are equivalent to bounded product hoops. Hoops are equivalent to BCK- \(\wedge \) -semilattices with the properties (P) and (Div). These equivalences, being structural and thus categorical, provide powerful tools for understanding hoops by leveraging the established theories of these related algebras. These relationships can be beneficial for individuals interested in any of the aforementioned algebraic structures.