Recent developments in the theoretical study of phase separation in manganites and underdoped cuprates

This paper is a brief review of the status of 'phase separation' ideas in manganites and cuprates, mainly focused on the recent efforts by the authors. It is argued that in the last year considerable progress has been made in the understanding of manganites, since the famous colossal magnetoresistance peak in the resistivity versus temperature has been numerically observed in unbiased Monte Carlo simulations using realistic models (namely, including double exchange, phonons, and quenched disorder). It is also conjectured that a phenomenology similar to the one found in manganites could be present in the underdoped regime of the cuprates. It is predicted that a state with superconducting patches exists above the critical temperature in the underdoped regime, in agreement with recent scanning tunneling microscopy experiments.