The pseudogap phase as a new state of matter will be explored in the phase string model of doped Mott insulators. It is composed of two distinct regimes known as the upper and lower pseudogap phases, respectively. The former corresponds to the condensate of resonating-valence-bond spin pairs and the latter is characterized by the formation of the Cooper pair amplitude. Elementary excitation in the latter is a spinon-vortex composite, which is charge-neutral object carrying spin-1/2 and vortex-like current. Such a lower pseudogap phase can be regarded as a vortex liquid state due to the presence of free spinon-vortices. Here thermally excited spinon-vortices destroy the phase coherence and are responsible for nontrivial Nernst effect and diamagnetism. The superconducting phase is closely related to the lower pseudogap phase by a topological transition with spinon-vortices and -antivortices forming bound pairs and the emergence of fermionic quasiparticles as holon-spinon-vortex bound objects. A quantitative phase diagram in the parameter space of doping, temperature, and magnetic field is determined and comparisons with experiments will be made.