The talk aims to discuss how to construct nonlocal PT-symmetric integrable equations from nonlocal group reductions of matrix spectral problems. Such nonlocal equations can be classified into three types: reserve space, reverse time, and reverse space-time, each of which can involve either the transpose or the Hermitian transpose. Notably there exist only five nonlocal PT-symmetric nonlinear Schrödinger and modified Korteweg-de Vires equations. Based on their associated spectral problems, a kind of Riemann-Hilbert problems are formulated and used to present the corresponding inverse scattering transforms. A solution formulation is proposed for special Riemann-Hilbert problems with the identity jump matrix and soliton solutions are generated within such a solution formulation.