This talk will be focused on inequalities involving bilinear operators in rearrangement-invariant spaces with weights. In particular, Young-type convolution inequalities of the form

[ \|f\ast g\|_Z \le C \|f\|_X \|g\|_Y ]

will be shown, with $X, Y, Z$ being various types of Lorentz spaces with general weights. Next, we will discuss more inequalities for bilinear versions of classical operators, above all Hardy-type operators, which may be obtained using similar techniques.