Derived category of coherent sheaves on an algebraic variety is one of
the most important and interesting algebraic invariants of the variety. When the
derived category of a variety is embedded into the derived category of other variety,
there are many interesting interactions between these two varieties. Especially there
are many  results about subcategories of derived categories of Fano varieties and
their interactions. Bondal asked whether derived category of every smooth projective
variety  can be embedded into derived categories of Fano varieties. We will discuss    
examples and recent progress of this question.