I will discuss two seemingly different but actually closely related unconventional quantum phase transitions: (I) A bandwidth tuned chiral spin liquid to topological superconductor transition. There is numerical evidence that there may be a chiral spin liquid(CSL) at finite U of half filled Hubbard model on triangular lattice. One natural phase nearby when closing the Mott gap through decreasing U is just a d+id topological superconductor (SC). We will provide three equivalent dual critical theories for the CSL to SC transition. One physical prediction is that there must exist critical CDW fluctuations at the QCP despite that CDW is absent in both phases. (II) In the second part, I will discuss possible phase transitions out of quantum Hall phases in twisted MoTe2 bilayer. Recently, there is a great experimental breakthrough in realizing fractional quantum hall phases at zero magnetic field in twisted MoTe2 bilayer due to the existence of a flat Chern band which mimics lowest landau level quite well at zero displacement field D=0. In this system tuning the displacement field D (through simply gating) changes the bandwidth and it is natural to expect a transition out of the quantum Hall phases to a conventional phase such as fermi liquid (FL) or some CDW states. At half filling, we will discuss a possible continuous composite fermi liquid (CFL) to Fermi liquid (FL) transition. The critical theory actually relies on the critical theory of CSL-SC transition in the first part as a building block which I will explain. Again a prediction is that there must be critical CDW fluctuations at the critical point. With disorder, we argue that the CDW fluctuations get pinned and the critical point in the clean limit becomes an intermediate CDW insulating phase, but with mobile neutral fermions inherited from the composite fermions in the CFL phase.