The family of pthalocyanine pigments, commonly called pthalos or thalos, come in a number of blue and green shades. They are beautiful, lightfast, transparent, and high in chroma. But I don't use them.
The reason is that they are too bloody strong. Pthalo blue is something like 40 times as strong a tinter as ultramarine blue. That means, for example, that in order to change the color of titanium white by 10%, you would add 40 times as much ultramarine blue as pthalo blue. That sounds like a good thing (efficient!), but in fact it's infuriating. In mixing, it is extraordinarily difficult to add a small enough amount of a pthalo color to get the effect you're looking for. Paint manufacturers reduce this problem somewhat by adding colorless extenders to some pthalo paints, but that only goes so far. Some artists learn to manage with pthalos (they are, in fact, quite popular artist's colors), but I hate trying to work with infinitesimal amounts of paint when trying to make subtle changes to mixtures, so they drive me nuts.
Fortunately, there are good substitutes. Prussian blue is almost exactly the same hue and transparency as a neutral (not green or violet) shade of pthalo blue, but a lot less strong. And viridian is very similar to a neutral pthalo green. So if you have trouble mixing with pthalo colors, try those instead.