The recent theoretical studies and experimental realizations of long-range interacting systems unveiled new striking phenomena, overcoming usual paradigms of the short-range physics. In my talk I exploit long-range generalizations of the Ising chain in a transverse field to illustrate some of these phenomena,as: i) the occurrence of nonlocal effects, like the lack of a maximum propagation velocity for a signal or the algebraic decay for correlation functions in gapped regimes, ii) the breakdown of conformal symmetry for continuous critical points, iii) the appearance of continuous phase transitions with nonvanishing mass gap, leading to new (families of) phases and new edge excitations, iv) the necessity to consider non standard decoupling hierachies in RG approaches. In spite of the relative simplicity of the assumed toy-models, the
described properties are inferred to be pretty general for long-range systems.
