I interpret your question to be asking about curve fitting techniques (for constructing fitted par/zero curves), since a term structure model (HW, LMM, etc.) can always be constructed to fit a given yield curve perfectly.
In an institutional setting, there really hasn't been any new models being proposed, because the existing ones are all very flexible and ...
Since contracts on physical goods have associated costs, it makes
sense that the term structure curve would be upward sloping. Since
there is no cost associated with delivery for the VIX and contango is
considered to exist in healthy markets, is the upward slope simply
accounting for the greater potential for the market to become
unhealthy over longer ...