Trees that cause shade
Some very large trees have extensive root networks below the soil that make it very difficult for other smaller shrubs to compete for water, nutrients and space. This is often the case under large Brazillian Pepper trees where we find very little seems to thrive. Here you could build up the soil above and amongst the roots and you may have more luck. Some trees also seem to cause the PH of the soil to change such as Pine trees, whose large drop of pine needles makes the soil too acidic for many plants to grow in. In this case use plants that are happy in these conditions such as various Plectranthus, Arums, Clivias, Crassulas.
Sandy shady soil
Sandy soil under trees is another common problem. The trees take many nutrients out of the soil which becomes depleted and hydrophobic meaning that water runs off it without penetrating to the roots of the plants. The answer to this is lots and lots of compost and organic mulch over the soil. You need to build up the proportion of decaying organic matter in the soil for it to become loamier and allowing water to penetrate easily.