The first result in this area was a theorem of Feldman who showed that closed curves without inflection points in Euclidean 3-space have exactly two regular homotopy classes, where regular homotopy means deformation through smooth immersions. Later, Gluck and Pan proved that knots without inflection points are isotopic through such knots provided that they are isotopic through general knots, and have the same self-linking number. The latter result follows from other theorems of Gluck and Pan on deformations of surfaces with boundary and positive curvature, which had been obtained by explicit constructions. In this talk we show how to use Gromov's h-principle, specifically the holonomic approximation theorem, to generalize these results to submanifolds with prescribed signs of principal curvatures and homotopy type of principal directions. Also, we show how convex integration techniques can be used to find knots with constant curvature or torsion in each isotopy class, and construct isotopies which keep the curvature or torsion of these knots constant.