In this talk, we propose alternative SDP, SOCP and LP approximation hierarchies to obtain global bounds for general polynomial optimization problems (POP), by using SOS, SDSOS and DSOS polynomials to strengthen existing LP hierarchy for POPs. Specifically, we show that the resulting approximations are substantially more effective in finding solutions of certain POPs for which the more common hierarchies of SDP relaxations are known to perform poorly. Numerical results based on the proposed hierarchies are presented on non-convex instances form the literature as well as on instances from the GLOBAL Library.