The standard \(\Lambda \) CDM model has been remarkably successful in explaining a wide range of cosmological observations, such as the cosmic microwave background (CMB) anisotropies, the large-scale structure of the Universe, and the accelerating expansion of the Universe. However, as the precision of cosmological measurements has improved, several significant tensions and anomalies have emerged. Chief among these is the Hubble tension, which refers to the discrepancy between local measurements of the Hubble constant ( \(H_0\) ) and the value inferred from CMB data assuming \(\Lambda \) CDM. This paper primarily focuses on the Hubble tension, exploring its origins, the extent of the discrepancy, and potential resolutions. Additionally, we discuss other emerging challenges to \(\Lambda \) CDM, such as the growth tension– the difference between the observed growth rate of cosmic structures and \(\Lambda \) CDM predictions– and various anomalies in the CMB, including the hemispherical power asymmetry, cosmic dipoles, and discrepancies in baryon acoustic oscillations (BAO). We review potential theoretical approaches to these challenges, including modifications to the model such as changes in dark energy physics, alterations in gravity, and fundamental physics transitions. The goal is to provide a comprehensive overview of the current status of these challenges, with a particular emphasis on the Hubble tension, and to discuss possible paths forward for resolving them. Upcoming cosmological surveys and experiments are expected to play a crucial role in addressing these tensions and enhancing our understanding of the Universe.