Recently, new types of tangential cones such as the radial tangent cone, the hypertangent cone, the Clarke's tangent cone, and the set of directions in which a set is epi-Lipschitzian at a point have been introduced by Clarke, Hiriart-Urruty, and Rockafellar. It turns out that in contrast to the classical tangential cones these new approximations are not necessarily isotone with respect to set inclusion. The present paper is concerned with modifications of the above-mentioned concepts that lead to isotone approximation. A concept of an approximation operator is introduced and a general scheme for construction of isotone approximations in real affine spaces is presented along with a survey of isotone approximations employed in optimization.