A rational Cherednik algebra is a flat deformation of a skew product of the Weyl algebra and a Coxeter group W. I am going to discuss two interesting subalgebras of Cherednik algebras going back to the work of Hakobyan and the speaker from 2015. They are flat deformations of skew products of quotients of the universal enveloping algebras of gl(n) and so(n), respectively, with W. I would also like to explain their relations with generalised Howe duality and geometry of particular nilpotent orbits.