Iterative shrinkage/thresholding (IST) algorithms are important elements of the computational toolbox used in signal processing and statistical inference problems, where sparse solutions are sought. Examples, include compressed sensing and signal/image restoration. IST algorithms are typically used to address unconstrained minimization formulations, where the objective function includes a quadratic data term (corresponding to liner observation model under Gaussian noise) and a non-quadratic regularizer (such as an l1 norm or a TV norm). In this talk, after briefly reviewing the several ways in which IST algorithms can be derived, as well as several convergence results, I will present some recent advances: (a) new ways to derive IST-like algorithms, (b) new accelerated versions of IST, (c) new IST-type algorithms tailored to non-Gaussian noise models.