  In 1999, S. V. Konyagin and V. N. Temlyakov introduced the so-called
Thresholding Greedy Algorithm. Since then, there have been many interesting and
useful characterizations of greedy-type bases in Banach spaces. In this
article, we study and extend several characterizations of greedy and almost
greedy bases in the literature. Along the way, we give various examples to
complement our main results. Furthermore, we propose a new version of the
so-called Weak Thresholding Greedy Algorithm (WTGA) and show that the
convergence of this new algorithm is equivalent to the convergence of the WTGA.
