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Abstract: The 'Thresholding Greedy Algorithm' was introduced by Konyagin and Temlyakov in order to study some special bases in Banach spaces. This basis is known as greedy basis and is characterized by unconditional and democratic properties of the basis. Later, Albiac, Dilworth, Kalton, Wojtaszczyk and few other author's studied the weaker versions of greedy basis, namely, almost greedy basis and partially greedy basis. Almost greedy basis can be characterized by quasi-greediness and democratic property and partially greedy basis can be characterized by quasi-greediness and conservative property. In this talk we will discuss some new characterizations of almost greedy and partially greedy basis. We will also discuss generalizations of greedy basis and its relatives. First part of this talk is joint work with Stephen J. Dilworth.