The clear importance of human induced pluripotent stem cell derived cardiomyocytes (hiPSC-CMs) as an in-vitro model highlights the relevance of studying these cells and their function also in-silico. Moreover, the phenotypical differences between the hiPSC-CM and adult myocyte action potentials (APs) call for understanding of how hiPSC-CMs are maturing towards adult myocytes. Using recently published experimental data, we developed two computational models of the hiPSC-CM AP, distinguishing between the ventricular-like and atrial-like phenotypes, emerging during the differentiation process of hiPSC-CMs. Also, we used the computational approach to quantitatively assess the role of ionic mechanisms which are likely responsible for the not completely mature phenotype of hiPSC-CMs. Our models reproduce the typical hiPSC-CM ventricular-like and atrial-like spontaneous APs and the response to prototypical current blockers, namely tetrodotoxine, nifedipine, E4041 and 3R4S-Chromanol 293B. Moreover, simulations using our ventricular-like model suggest that the interplay of immature I Na, I f and I K1 currents has a fundamental role in the hiPSC-CM spontaneous beating whereas a negative shift in I CaL activation causes the observed long lasting AP. In conclusion, this work provides two novel tools useful in investigating the electrophysiological features of hiPSC-CMs, whose importance is growing fast as in-vitro models for pharmacological studies.