Abstract: We discuss moment and tail estimates for Gaussian chaoses with values in Banach spaces. We formulate a conjecture regarding two-sided estimates and show that it holds in a certain class of Banach spaces including L_q spaces. As one of corollaries we present upper bounds for tails and moments of quadratic forms in subgaussian random variables, which extend the Hanson-Wright inequality. (talk is based on a joint work with Radoslaw Adamczak and Rafal Meller)