This paper reports on the synthesis and characterization of a series of amphiphilic polymers which exhibit spectacular reversible shear-induced gelation in water. The systems consist of hydrophobically modified copolymers based on N,N-dimethylacrylamide and acrylic acid. The influence of molecular parameters such as the molecular weight and composition of the terpolymers on the rheological properties has been established. In the linear regime, the polymers behave like classical associating polymers: the sharp increase of the viscosity with concentration is the result of the transformation of intra- into intermolecular associations. Moreover, the dynamics of the physical gels obtained at high concentrations is tremendously slowed by the presence of alkyl side chains. Under shear the solutions display a Newtonian plateau at low shear rate followed by a shear-induced gelation. The latter is characterized in terms of a critical shear rate which sharply decreases as the polymer volume fraction increases. Thus, it appears that the shear-induced gelation may be controlled by adjusting the polymer molecular features. The networks built under shear closely behave like highly concentrated solutions at rest, suggesting a possible parallel between increasing shear and increasing concentration. This latter fact is reminiscent of the situation encountered with wormlike micelles. Shear flow could induce a transition between individual aggregates and a transient network as an increase in concentration does, thanks to the sharp modification of the electrostatic screening at the overlap concentration.