The talk will survey some recent results related by the common theme of finding rank-one connections between energy wells in nonlinear elasticity models of crystals. It will cover three cases (i) slip and twinning in Bravais lattices using the Ericksen energy-well picture, (ii)  compatibility of martensitic microstructures across polycrystal grain boundaries and the Taylor set (joint with M. Galanopoulou), and (iii) remarkable martensitic microstructures observed in the alloy Ti_76 Nb_22 A_l2, and their interpretation in terms of T_N configurations (joint with T. Inamura & F. Della Porta).