We examine the potentiality of both CERN LEP and Fermilab Tevatron colliders to establish bounds on new couplings involving the bosonic sector of the standard model. We pay particular attention to the anomalous Higgs interactions with $\gamma$, $W^{\pm}$ and $Z^0$. A combined exclusion plot for the coefficients of different anomalous operators is presented. The sensitivity that can be achieved at the Next Linear Collider and at the upgraded Tevatron is briefly discussed.