Liquid crystalline polymers in nematic solvents are studied theoretically. Three different scenarios are discussed: (i) confined polymers; (ii) grafted polymers and (iii) double brushes. The competition between nematic distortion, chain elasticity, excluded volume and nematic anchoring enables these systems to exhibit a number of remarkable properties. Notably, they can undergo tilting and anchoring transitions and show a quasi-piezoelectric effect. These phenomena may have applications in the design of liquid crystal displays and in making smart electro-optic, mechano-optic and electromechanic materials.