With the in-depth understanding of nano-/micro-scaled systems and the developing of the corresponding experimental techniques, the heat transport and energy conversion processes in these small systems have attracted much interest recently. In contrast to the static manipulation methods, which hinge on the steady nonequilibrium sources such as temperature bias, chemical potential difference, etc., the temporal driving methods can control small systems in nonequilibrium non-steady states with much more versatility and universality. The research on periodically driven small systems holds both fundamental and pragmatic promises. This review is based on the fundamental concept of geometry. By analyzing the geometric phase and thermodynamic length in the transport process and the energy conversion process, we provide a unified perspective for the recent researches on the thermodynamic properties of driven nonequilibrium quantum systems. Thermodynamic geometry not only is the intrinsic origin of the nontrivial transport and dissipation, but also provides us with an all-applicable theoretical framework. The discussion over the geometry would yield multiple thermodynamic constraints on the transport and energy conversion, and can naturally construct a general optimization method as well. This will conduce to a better understanding of functionality for nonequilibrium quantum many-body systems acting as thermal machines. Also, this will inspire people to design quantum thermal machines with simultaneously more ideal performance, i.e. higher efficiency, higher power and higher constancy.