A \(q\)-integral \(\int_0^\infty a(t)\,d_qt\) is called summable (A) to the value \(S\) if the \(q\)-Laplace integral \(f(x)=\int_0^\infty e_q^{-xt} a(t)\,d_qt\) converges for every \(x>0\) and \(\lim_{x\rightarrow 0^+} f(x)=S\). The authors study summability of \(q\)-integrals and prove some related Tauberian theorems.