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This is a survey of author's results on weight structures and Voevodsky'smotives. Weight structures are natural counterparts of t-structures (fortriangulated categories) introduced by the author. They allow to constructweight complexes, weight filtrations, and weight spectral sequences for variouscohomology theories. Partial cases of the latter are: 'classical' weightspectral sequences (for singular and etale cohomology), coniveau spectralsequences, and Atiyah-Hirzebruch spectral sequences. All of those are mentionedin the current paper. The details, proofs, and several more results could befound in other papers of the author (cited here). We also mention a certaintriangulated category of comotives that contains reasonable (co)motives for allfunction fields (and also of other projective limits of smooth varieties).

Weight structures and motives; comotives, coniveau and Chow-weight spectral sequences, and mixed complexes of sheaves: a survey