SVV models, or Sandwiched Volterra Volatility models, are a class of dynamics able to capture both the long memory and the rough aspects of volatility as well as complying with several typical stylised features of volatilities. At the same time, they are treatable enough to allow for a rigorous and explicit analysis of pricing and hedging. We present this class of models with their features and potentials. We discuss pricing and hedging of financial derivatives in this framework. Specifically, we focus on the quadratic hedging approach, providing insight on the computational challenges related to the optimal strategy. The explicit optimal hedging solution is identified by means of the non-anticipating derivative, while its numerical counterpart is articulated by means of Markovian approximations.