Attosecond ionization dynamics, a central topic in ultrafast science, largely depends on advances in experimental techniques and theoretical modeling to reveal the fundamental processes that control the evolution of matter on an ultrafast timescale. Among the cutting-edge approaches in this field, the strong-field multiphoton transition interferometry (SFMPTI) method stands out due to its ability to detect multiphoton ionization dynamics with attosecond time resolution via quantum path interference. This technique has been widely applied to the attosecond-scale measurements and characterizations of ionization time delays with quantum-state specificity, ranging from atomic systems to complex molecules. It provides a novel time-domain perspective in the study of strong-field physics. This article focuses on the application of the SFMPTI in probing strong-field multiphoton ionization time delays in atoms and molecules. We systematically present the quantum interference mechanisms behind the method: electrons undergo multi-photon above-threshold ionization (ATI) driven by a 400 nm laser pulse, while an additional 800 nm laser pulse induces the sideband signals through two-color interference. The relative phases encoding of these sidebands provides precise timing information about the ionization process. Furthermore, we summarize the recent advances in attosecond-resolved investigations of ATI dynamics and resonance-state-mediated time delays. For instance, the significant influence of resonance-enhanced multiphoton ionization processes involving different intermediate states in Ar atoms on ionization time delays is elucidated, highlighting the important influences of Freeman resonances on photoelectron emission dynamics in strong laser fields. Additionally, nuclear vibrations in NO molecules change ionization trajectories via nonadiabatic coupling of potential energy surfaces, leading to variations in time delay. Notably, the substantial influence of internuclear distance on ionization delay highlights the high sensitivity of electron-nuclear co-evolution to ultrafast phenomena. Finally, we discuss the potential applications and remaining challenges of this emerging technique, which will continue to open up new avenues for exploring attosecond electron dynamics in complex systems.