<p>This work presents a brief overview of bases and basic sequences criteria in topological vector spaces. While the theory in normed spaces is well established, the study of such sequences in more general spaces is scarce in the literature. Our main goal is to present the Banach-Grumblum-Nikolskii criterion for basic sequences in general settings that are not necessarily locally convex, such as <i>F</i>-spaces and quasi-Banach spaces.</p>