Experimental and theoretical aspects of obtaining the magnetic information carried by laser beams diffracted from an array of micro- or nanosized magnetic objects are reviewed. We report on the fundamentals of vector magneto-optic Kerr effect (MOKE), Bragg-MOKE, and second-order effects in the Kerr signal in longitudinal Kerr geometry as well as on an experimental setup used for vector and Bragg-MOKE experiments. The vector and Bragg-MOKE technique in combination with micromagnetic simulation is a reliable tool for measuring the complete magnetization vector and for characterizing the reversal mechanism of lateral magnetic nanostructures. We discuss the Bragg-MOKE effect for three standard domain configurations during the magnetization reversal process and present the expected behavior of the magnetic hysteresis loops.