Aims. Stellar activity data provide evidence of activity wave branches propagating polewards rather than equatorwards (the solar case). This evidence is especially pronounced for the well-observed subgiant HR 1099. Stellar dynamo theory allows polewards propagating dynamo waves for certain governing parameters. In this paper, we try to unite observations and theory. Methods. Taking into account the preliminary stage both of observations of polar activity branches and of the determination of the governing parameters for stellar dynamos, we restrict our investigation to the simplest mean-field dynamo models, while recognizing more modern approaches to be an essential development. Results. We suggest a crude preliminary systematization of the reported cases of polar activity branches. Then we present results of dynamo model simulations which contain magnetic structures with polar dynamo waves, and identify the models which look most promising for explaining the latitudinal distribution of spots in dwarf stars. Those models require specific features of stellar rotation laws, and so observations of polar activity branches may constrain internal stellar rotation. Specifically, we find it unlikely that a pronounced poleward branch can be associated with a solar-like internal rotation profile, while it can be more readily reproduced in the case of a cylindrical rotation law appropriate for fast rotators. We stress the case of the subgiant component of the active close binary HR 1099 which, being best investigated, presents the most severe problems for a dynamo interpretation. Our best model requires dynamo action in two layers separated in radius. This interpretation requires some change in the paradigm of stellar magnetic studies, as it explains surface manifestations in a subgiant as a joint effect of shallow and deep layers of the stellar convective zone, rather than of a surface magnetic field only, as appears to be the case in dwarf stars. Conclusions. Observations of polar activity branches provide valuable information for understanding stellar activity mechanisms and internal rotation, and thus deserve intensive observational and theoretical investigation. Current stellar dynamo theory seems sufficiently robust to accommodate the phenomenology.