Abstract 

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In this talk I will give an overview over a still growing series of papers with 
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Niels Kowalzig in which we study algebraic structures that are present on 

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(co)homology theories that can be expressed as Ext and Tor over Hopf algebroids, 

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such as Hochschild, group, Lie algebra, or Poisson (co)homology. I will spend 

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some time explaining what I mean by a Hopf algebroid, and then discuss structures 

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such as cup and cap products, Gerstenhaber brackets, cyclic homology, and 

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Poincare-type dualities, that can all be studied in a unified manner.