The phenomenon of magnetoresistivity is known since the days of Michael Faraday when he observed nearly 1-2% change in electrical resistivity under a magnetic field in glassy materials. Over the years, while new materials with varying degrees of magnetoresistivity have been developed, the quest for unearthing the mechanism, side by side, led to the formulation of new theories for more complex materials with complicated electronic band structure courtesy local magnetic interaction and strong correlation. Following Kramer's concept of indirect magnetic exchange interaction, the formulation of double exchange interaction theory in the 1950'2, by Zener, Anderson, and de Gennes, created a perspective for analyzing the correlation between metallic charge conduction and ferromagnetism and hence a sizable magnetoresistivity - observed in a series of transition metal oxides with different crystallographic structures. During the last one and a half decade, a series of unusual and unexpected observations have been made in different compounds - (a) giant negative magnetoresistivity in magnetic multilayers, (b) even higher and therefore colossal magnetoresistivity in single phase doped LaMnO3 based compounds, (c) melting of a certain charge state under a magnetic field, (d) magnetic field driven structural phase transition and a large change in resistivity thereby, to name just a few. This review discusses the traditional concepts starting from classical Hall effect to domain boundary interaction to Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism and places the more recent developments against the backdrop of old concepts. It also looks beyond double exchange plus Jahn-Teller effect into the modern theory of finer scale intrinsic phase separation and percolation conduction as the most probable scenario for describing the magnetoresistivity in various transition metal oxides. The limited application potential of magnetoresistivity seems to have now become unlimited with the jump in the magnitude of magnetoresistivity. This review presents a few glimpses of new possibilities and future scopes.
