We review a family of model selection techniques called thresholding that assume the vector of parameters has few non-zero coefficients, and we show two applications of thresholding estimators. First, we derive a new class of statistical tests for generalized linear models. These tests can be employed whether the model includes more parameters than observations or not. We show through simulations that our tests have better control of the nominal level and higher power than existing tests. Second, we use a thresholding estimator to solve a cosmology problem that consists in recovering the 3D gas emissivity of a galaxy cluster from a 2D image taken by a telescope. We perform simulations in which we show how our methodology outperforms the current state-of-the-art approach in terms of mean squared errors, and how it has good coverage probability. We apply our methods to five different real telescope images and discuss the scientific findings.