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We describe the Voevodsky's category $DM^{eff}_{gm}$ of motives in terms ofSuslin complexes of smooth projective varieties. This shows that Voeovodsky's$DM_{gm}$ is anti-equivalent to Hanamura's one. We give a description of anytriangulated subcategory of $DM^{eff}_{gm}$ (including the category ofeffective mixed Tate motives). We descibe 'truncation' functors $t_N$ for$N>0$. $t=t_0$ generalizes the weight complex of Soule and Gillet; its targetis $K^b(Chow_{eff})$; it calculates $K_0(DM^{eff}_{gm})$, and checks whether amotive is a mixed Tate one. $t_N$ give a weight filtration and a 'motivicdescent spectral sequence' for a large class of realizations, including the'standard' ones and motivic cohomology. This gives a new filtration for themotivic cohomology of a motif. For 'standard realizations' for $l,s\ge 0$ wehave a nice description of $W_{l+s}H^i/W_{l-1}H^i(X)$ in terms of $t_s(X)$.  We define the 'length of a motif' that (modulo standard conjectures)coincides with the 'total' length of the weight filtration of singularcohomology. Over a finite field $t_0Q$ is (modulo Beilinson-Parshin conjecture)an equivalence.Comment: Several linguistic corrections made; section 2.3 was corrected als

Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky versus Hanamura