The theory of viscosity solutions, initiated in the early 80 an extremely convenient PDE framework for dealing with the lack of smoothness of the solutions to fully nonlinear first and second order equations. This theory provides a body of simple and effective techniques for ascertaining the existence, uniqueness, and stability of solutions for certain nonlinear equations via maximum principle type arguments entailing smooth test functions. The scope of the theory is quite broad and one of the main applications is the homogenization of fully nonlinear equations. The approach to homogenization of nonlinear equations by viscosity solutions methods begins with the pioneering unpublished paper by Lions, Papanicolau & Varadhan[5] that introduced the effective Hamiltonian and gave the first convergence result for Hamilton-Jacobi equations. The convergence proof was then simplified and extended to second-order equations by Evans[3, 4]. The theory of homogenization was then continued by many authors to cover a number of different issues. In this talk we will describe some viscosity methods and techniques to study periodic homogenization of fully nonlinear PDEs in Rn . We will also present some recent results obtained in a joint work with G. Barles. P.L. Lions and P. Souganidis [1] about periodic homogenization of elliptic and parabolic boundary value problems in half-space type domains with Neumann boundary conditions. [1] G.Barles, F. Da Lio, Francesca, P.L. Lions, P. Souganidis. Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions. to appear in Indiana Univ. Math. J. [2] M.G. Crandall, P.L. Lions. Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983), no. 1, 1-42. [3] L.C. Evans.The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), no. 3-4, 359 [4] L.C. Evans.Periodic homogenization of certain fully nonlinear partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), no. 3-4, 245 [5] P.L Lions, G. Papanicolau, S. Varadhan. Homogenization of Hamilton-Jacobi equations. Unpublished.