I will discuss our recent studies at RHIC and LHC based on a multiphase transport (AMPT) model, mainly including initial fluctuations and di-hadron correlations, the specific shear viscosity of quark-gluon plasma (QGP), and the elliptic flow (v2) splitting of particles and their antiparticles in the Beam-Energy Scan (BES) program. We found that the triangular flow and higher-order harmonic flows, which originate from initial density fluctuations, contribute significantly to the away-side double-peak structure of di-hadron correlations. In addition, both short-range and long-range di-hadron correlations are studied at LHC, and they are qualitatively consistent with experimental results from the CMS Collaboration. Furthermore, with the same parameter set for the Lund string fragmentation function and the parton scattering cross section at both RHIC and LHC, the charged particle multiplicities and the harmonic flows can be reasonably reproduced comparing to the experimental data. The specific shear viscosities of QGP extracted from AMPT model studies at both RHIC and LHC are compared with results from other approaches. To explain the v2 splitting between particles and their antiparticles in the BES program at RHIC, the Nambu-Jona-Lasinio model is used to describe the partonic phase in AMPT, while the mean-field potentials are introduced to both the partonic and the hadronic phase. The study demonstrates that the quark vector interaction plays an important role in quantitatively explaining the v2 splitting between particles and their antiparticles, while the former affects the QCD phase structure and the site of the critical point of hadron-quark phase transition.