The Viper incarnation of the character appears in the show. She first appears as one of Baron Strucker's right hand lieutenants. At some unknown point, Viper was captured and supplanted by a Skrull who infiltrated into the HYDRA ranks. The Skrull's capture was Nick Fury's first hint of an upcoming Skrull invasion.
The actual Viper was the first of the Skrulls' prisoners Captain America found when he was escaping himself. They freed the other prisoners (one of them her second-in-command King Cobra) and escaped together, with Viper even taking Cap on board the escape ship when it seemed he was going to be left behind.
After the Skrull invasion was over, Viper and King Cobra were transported as prisoners by armored truck, but the rest of the Serpent Society arrived to break them out, which resulted on them trapped in the subway alongside Captain America, Spider-Man and civilian bystanders. Cap and Spidey managed to protect the bystanders from the Serpent Society.
The Marvel Cinematic Universe iteration is an artificial intelligence entity, who takes on the alias of Madame Hydra, after transferring her consciousness into the Framework. She is well aware of her alternate identity, referring to the real world as 'The Other Place'.