Hello forum!
Can anyone provide me with insight as to how we get the garden plants we have today? Do breeding companies simply select plants, breed them, grow the seeds, and then propagate the plants? Or is their genetic engineering involved? Are the "new" varieties that are released annually "created" or breed? Hearing the words genetic engineering or GMO gives me the icks.

The answer is yes to all those possibilities, anf more. It will depend on the particular plant(s). Some are engineered, some are bred, some are selected, some are treated with chemicals, etc.

But GMOs are very rare in ornamental plant, trees and shrubs.

Many aroids that get tissue cultured get 'selected'. One of the best examples is Alocasia reginula, the now very popular alocasia with black velvety looking leaves. Before it was tissue cultured it was propagated by division and simply called Alocasia reginula. Then a tc company here in Florida 'selected' a cloned specimen that they thought had superior qualities and focused on reproduction of that single specimen and named their new plant Alocasia'Black Velvet'. So now no one who collected plants before Black Velvet existed knows it was not always called that