Effective Field Theory (EFT) is a powerful framework for systematically improving calculations in physical systems with a separation of scales. In few-body systems with short-range interactions and large two-body scattering length, universal features emerge. For systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization at leading order. This review discusses the application of EFT in cold atom and nuclear physics, including the possibility of an infrared limit cycle in QCD. Recent extensions of EFT to four-body systems and N-boson droplets in two spatial dimensions are also addressed. The EFT for three-body systems with large scattering length a is discussed, showing that two parameters are needed: the scattering length a and the three-body parameter Λ*. The three-body binding energies are determined by the values of E < 0 for which the homogeneous version of the equation has a nontrivial solution. The three-body coupling H is periodic and runs on a limit cycle, indicating discrete scale invariance. This is a signature of an RG limit cycle. Universal properties of few-body systems with large scattering length are discussed, including the Efimov effect, where infinitely many three-body bound states accumulate at threshold. The ratio of binding energies of successively shallower states approaches a constant λ₀² ≈ 515. Universality also constrains three-body scattering observables, such as the atom-dimer scattering length, which can be expressed in terms of a and Λ*. In two spatial dimensions, the universal properties of weakly interacting bosons with large scattering length are discussed. The size of the N-body droplet decreases exponentially with N, while the binding energy increases exponentially. The ratio of binding energies of successive states approaches a constant value. These properties are valid for N large but below a critical value. The success of pionless EFT demonstrates that physical QCD is close to an infrared limit cycle. Adjusting the quark masses could tune QCD to this limit cycle, leading to the Efimov effect for the triton. In two dimensions, the three-body parameter Λ* does not enter at leading order, and N-body binding energies depend only on B₂. The asymptotic freedom of non-relativistic bosons with attractive interactions in 2D leads to remarkable universal properties of N-body droplets. The three-body effects discussed are also relevant in Fermi systems with three or more spin states. Future challenges include universality in the N-body problem for N ≥ 4, effective range corrections, and large scattering lengths in higher partial waves. A large P-wave scattering length appears in nuclear halo systems such as ⁶He.Effective Field Theory (EFT) is a powerful framework for systematically improving calculations in physical systems with a separation of scales. In few-body systems with short-range interactions and large two-body scattering length, universal features emerge. For systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization at leading order. This review discusses the application of EFT in cold atom and nuclear physics, including the possibility of an infrared limit cycle in QCD. Recent extensions of EFT to four-body systems and N-boson droplets in two spatial dimensions are also addressed. The EFT for three-body systems with large scattering length a is discussed, showing that two parameters are needed: the scattering length a and the three-body parameter Λ*. The three-body binding energies are determined by the values of E < 0 for which the homogeneous version of the equation has a nontrivial solution. The three-body coupling H is periodic and runs on a limit cycle, indicating discrete scale invariance. This is a signature of an RG limit cycle. Universal properties of few-body systems with large scattering length are discussed, including the Efimov effect, where infinitely many three-body bound states accumulate at threshold. The ratio of binding energies of successively shallower states approaches a constant λ₀² ≈ 515. Universality also constrains three-body scattering observables, such as the atom-dimer scattering length, which can be expressed in terms of a and Λ*. In two spatial dimensions, the universal properties of weakly interacting bosons with large scattering length are discussed. The size of the N-body droplet decreases exponentially with N, while the binding energy increases exponentially. The ratio of binding energies of successive states approaches a constant value. These properties are valid for N large but below a critical value. The success of pionless EFT demonstrates that physical QCD is close to an infrared limit cycle. Adjusting the quark masses could tune QCD to this limit cycle, leading to the Efimov effect for the triton. In two dimensions, the three-body parameter Λ* does not enter at leading order, and N-body binding energies depend only on B₂. The asymptotic freedom of non-relativistic bosons with attractive interactions in 2D leads to remarkable universal properties of N-body droplets. The three-body effects discussed are also relevant in Fermi systems with three or more spin states. Future challenges include universality in the N-body problem for N ≥ 4, effective range corrections, and large scattering lengths in higher partial waves. A large P-wave scattering length appears in nuclear halo systems such as ⁶He.