  Aperiodic dynamics which is nonchaotic is realized on Strange Nonchaotic
attractors (SNAs). Such attractors are generic in quasiperiodically driven
nonlinear systems, and like strange attractors, are geometrically fractal. The
largest Lyapunov exponent is zero or negative: trajectories do not show
exponential sensitivity to initial conditions. In recent years, SNAs have been
seen in a number of diverse experimental situations ranging from
quasiperiodically driven mechanical or electronic systems to plasma discharges.
An important connection is the equivalence between a quasiperiodically driven
system and the Schr\"odinger equation for a particle in a related quasiperiodic
potential, giving a correspondence between the localized states of the quantum
problem with SNAs in the related dynamical system. In this review we discuss
the main conceptual issues in the study of SNAs, including the different
bifurcations or routes for the creation of such attractors, the methods of
characterization, and the nature of dynamical transitions in quasiperiodically
forced systems. The variation of the Lyapunov exponent, and the qualitative and
quantitative aspects of its local fluctuation properties, has emerged as an
important means of studying fractal attractors, and this analysis finds useful
application here. The ubiquity of such attractors, in conjunction with their
several unusual properties, suggest novel applications.
