The Poisson σ-models are described, as well as the σ-models connected by the Poisson-Lie T-duality. Common algebraic structures are emphasized, as the models are investigated from the geometrical point of view. The possibility to introduce a duality transformation of the Poisson-Lie σ-models is discussed. A general method, which enables one to construct a Poisson-Lie sigma model using an arbitrary Lie bialgebra, is given. The correspondence to the the R~2 gravity action is shown, as well as other physically relevant examples of the Poisson-Lie sigma models.
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