Understanding the intergalactic medium is crucial for comprehending galaxy formation and evolution in the universe. While our theoretical understanding of the high-redshift intergalactic medium (z>3) aligns well with observations, the low-z intergalactic medium (z<1) presents significant challenges. Observations reveal that over 30% of the gas predicted by the standard model of the Universe remains unaccounted for, and the distribution of Doppler widths in the low-z Lyman alpha forest eludes accurate reproduction in all existing simulations. There is still an unexplored void spanning 5 to 10 billion years of cosmic time where measurements of the UV ionizing background and the thermal state of the intergalactic medium are lacking. Additionally, the impact of galaxy formation feedback on the intergalactic medium, particularly at low redshifts, cannot be ignored. In this talk, the speaker will address these pressing issues, focusing on the importance of the UV background, the influence of AGN feedback, and the associated challenges for studying the low-z intergalactic medium.