In this paper, we study the defocusing energy-critical nonlinear Schrödinger equations i∂ t u + ∆u = |u| 4 d−2 u. When d = 3, 4, we prove the almost sure scattering for the equations with nonradial data in H s x for any s ∈ R. In particular, our result does not rely on any spherical symmetry, size or regularity restrictions. Contents 1. Introduction 1.1. Definition of randomization 1.2. Main result 1.3. Sketch of the proof. 1.4. Organization of the paper 2. Preliminary 2.1. Notation 2.2. Useful lemmas 2.3. Probabilistic theory 3. Almost sure Strichartz estimates 3.1. Strichartz estimates 3.2. Linear estimates in 3D case 3.3. Linear estimates in 4D case 4. Global well-posedness and scattering in 3D case 4.1. Reduction to the deterministic problem 4.2. Local theory 4.3. Modified Interaction Morawetz 4.4. Almost conservation law 4.5. Perturbations 4.6. Proof of Proposition 4.1 5. Global well-posedness and scattering in 4D case 5.1. Reduction to the deterministic problem 5.