  The geometric properties of sigma models with target space a Jacobi manifold
are investigated. In their basic formulation, these are topological field
theories - recently introduced by the authors - which share and generalise
relevant features of Poisson sigma models, such as gauge invariance under
diffeomorphisms and finite dimension of the reduced phase space. After
reviewing the main novelties and peculiarities of these models, we perform a
detailed analysis of constraints and ensuing gauge symmetries in the
Hamiltonian approach. Contact manifolds as well as locally conformal symplectic
manifolds are discussed, as main instances of Jacobi manifolds.
