I will explain two ways of quantizing compact symmetric spaces. The
first is due to Letzter and Kolb, giving explicit generators of the dual
coideal. The second is essentially due to Enriquez and Etingof, and
relies on cyclotomic Knizhnik-Zamolodchikov equations. Both approaches
make sense in the formal and analytic (0</q/<1) settings. They are
equivalent in a suitable sense for the sphere, therefore giving two ways
of looking at Podleś spheres. In the formal setting, we can now show
that they are equivalent in general. (Joint work with Kenny De Commer,
Lars Tuset and Makoto Yamashita.)