Recent results on particle momentum and spin correlations are discussed, particularly, in view of the role played by the effect of final state interaction. It is demonstrated that this effect allows for (i) correlation femtoscopy with unlike particles; (ii) study of the relative space-time asymmetries in the production of different particle species (including relative time delays); (iii) study of the particle strong interaction hardly accessible by other means (e.g., in ΛΛ system).