Exploiting spatial information in high-dimensional inference promises to improve the accuracy of statistical procedures. This article develops a new class of spatially adaptive false discovery rate thresholding (SAFT) procedure by extending the elegant false discovery rate thresholding estimator (Abramovich et al., 2006) to spatial settings. The idea is first constructing robust and structured-adaptive weights via estimating the local sparsity levels, and then setting spatially adaptive thresholds through weighted Benjamini-Hochberg (BH) Procedure. SAFT procedure is data-driven and assumption- lean. Theoretical results demonstrate the superior asymptotic performance over the original false discovery rate thresholding estimator in spatial settings. The finite sample performance is studied using both simulated data and real data, which shows the proposed SAFT procedure outperforms the existing methods in various settings. Joint work with Jiajun Luo, Gourab Mukherjee and Yunjin Choi.