Luminous Star Clusters (SCs) are fundamental building blocks of galaxies, and they provide basic information regarding the mechanisms of star formation and the process of galaxy formation and evolution. In my PhD thesis project I investigated properties of young SCs in a sample of 87 nearby Luminous Infrared Galaxies (LIRGs: LIR>10^11 L_sun) imaged with the Hubble Space Telescope's Advanced Camera for Surveys at 0.4¶æm (F435W) and 0.9¶æm (F814W). Many LIRGs are observed to be ongoing mergers of gas-rich disk galaxies. They contain extreme starbursts and hence are expected to host particularly rich and luminous populations of SCs. This project represents the largest sample of galaxies with uniformly characterized properties of their SC population. The size of the sample allows an identification of trends in SC properties with merger stage and star formation rate. A large fraction (~17%) of the cluster population is younger than 10 Myr. There is uncertainty in the determination of the ages of the bulk of the SCs due to an age-extinction degeneracy - the majority of the detected cluster population may have ages of up to a few hundred Myr. The median SC luminosity function index of the LIRG sample is alpha=-1.8, which is in a good agreement with previously published studies in various galaxy types. This sample contains some of the most luminous clusters observed so far, with Mmax (F435W) exceeding -17 mag. LIRGs follow the brightest cluster - star formation rate correlation observed for lower luminosity star-forming galaxies quite closely, although a large degree of scatter possibly due to extinction and over-estimation of Star Formation Rates (SFRs) in galaxies containing an Active Galactic Nucleus (AGN) is present. Thus, the size-of sample effect and the observed high SFRs are responsible for high luminosity of SCs found in LIRGs. The specific luminosity TL(F435W) - SFR(far-IR + far-UV) relation observed for nearby non-interacting spiral galaxies is not applicable to LIRGs. However, a weak correlation of specific luminosity TL(F435W) - SFR(far-UV) is apparent. No clear trend of SC properties with the merger stage of the LIRG is observed; although in late merger stages the degree of the extended star formation diminishes and the centrally concentrated nuclear starburst or an AGN dominate the energy output of the LIRG. Galaxies with HII-region like (i.e., starburst like) nuclear spectra exhibit higher specific frequency TN, specific luminosity TL and Mmax (F435W) values compared to galaxies where an AGN is present. In a sub-sample of the 15 most cluster-rich LIRG systems, auto-correlation functions reveal a hierarchical spatial distribution of SCs; correlation functions with GALEX near-UV and Spitzer IRAC 8¶æm images show an overlap of near-UV emission and locations of optically visible clusters and no apparent correlation with mid-IR emission (i.e., embedded star formation). Thus, optically visible young SCs and UV emission represent un-obscured star formation which appears to be unassociated with the bulk of the star formation that takes place in dusty central regions of LIRGs.