Given two Banach spaces $X$ and $Y$, we analyze when the projective tensor product $X\widehat{\otimes}_��Y$ has Corson's property (C) or is weakly Lindel��f determined (WLD), subspace of a weakly compactly generated (WCG) space or subspace of a Hilbert generated space. For instance, we show that: (i) $X\widehat{\otimes}_��Y$ is WLD if and only if both $X$ and $Y$ are WLD and all operators from $X$ to $Y^*$ and from $Y$ to $X^*$ have separable range; (ii) $X\widehat{\otimes}_��Y$ is subspace of a WCG space if the same holds for both $X$ and $Y$ under the assumption that every operator from $X$ to $Y^*$ is compact; (iii) $\ell_p(��)\widehat{\otimes}_��\ell_q(��)$ is subspace of a Hilbert generated space for any $1< p,q