Different methods of generating and detecting propagating solitons in uniform and nonuniform, steady and unsteady shearing nematic liquid crystals are proposed, reviewed, and discussed in detail. These include the use of (1) an external plate moving uniformly in the middle and at one end of the liquid crystal (LC) cell, (2) a LC cell with one glass plate moving uniformly and reversing in direction, (3) an external plate as in (1) but moving periodically, (4) pressure gradients along the long axis of the LC cell, (5) circular LC cell with one glass plate rotating, and (6) circular LC cell with radial pressure gradients. In each of these cases, the relevant equations of motion of the LC molecules are derived and analyzed. In the essentially one-deminsional cases of (1) to (3), the governing equation is the damped, driven since-Gorden equation. Analytic and numerical results of single and multisolitons are presented. A multiscale perturbation method is used in the unsteady case of (4). The related case of "soliton switch" in ferroelectric smectic C* is discussed.