Resonances give rise to the most interesting features in atomic photoionization spectra. Over the past forty years, the study of these resonances has stimulated much excitement in theories as well as in experiments. The close agreement finally achieved between theory and experiment has verified the predictions of the theory which in turn lead to better understanding of the physical process and advances the knowledge on the physical system. In this work, we will discuss some of the advances made in this area for low-Z atomic systems with emphasis on the lithium atom as an example. In particular, we will discuss the calculation of resonance parameters using the saddle-point method and saddle-point complex method.