The interaction of flexible polymers with fluid flows leads to a number of intriguing phenomena observed in laboratory experiments, namely drag reduction, elastic turbulence, and heat transport modification in natural convection, and is one of the most challenging subjects in soft matter physics. In this review, we examine our present knowledge on the subject. Our present knowledge is mostly based on direct numerical simulations performed in the last twenty years, which have successfully explained, at least qualitatively, most of the experimental results. Our goal is to disentangle as much as possible the basic mechanisms acting in the system in order to capture the basic features underlying different theoretical approaches and explanations.

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