In this talk I introduce nonlocal (infinite-derivative) field theories. First of all, I show how and which principles of standard quantum field theory are affected when higher-order derivative operators are taken into account in the Lagrangian. In particular, I focus on the issue of unitarity and on how to make higher-derivative theories healthy by means of non-polynomial differential operators. Subsequently, I consider the gravity sector and construct a nonlocal theory whose graviton propagator is ghost-free, and explore the possibility to regularize singularities. Finally, I make a comparison among different nonlocal differential operators which satisfy the ghost-free condition, and also discuss some phenomenological implications.