Compressed sensing is a signal acquisition paradigm that utilizes the sparsity of a signal (a vector in $R^N$ with $s << N$ non-zero entries ) to efficiently reconstruct it from very few (say n, $s < n << N$) generalized linear measurements. These measurements often take the form of inner products with random vectors drawn from appropriate distributions, and the reconstruction is typically done using convex optimization algorithms or computationally efficient greedy algorithms. In this talk we cover some recent results in compressed sensing and related areas where the signal acquisition is also done via such generalized linear measurements. We discuss signal recovery from compressed sensing measurements using weighted $\ell_1$ minimization, when erroneous support information is available. We provide reconstruction guarantees that hold with high probability and improve on the standard results, provided the support information is accurate enough. TIme permitting, we also discuss some recent results on the digitization of generalized linear measurements, including compressed sensing measurements.