This review focuses on the light-harvesting properties of photosystem I (PSI) and its LHCI outer antenna. LHCI consists of different chlorophyll a/b binding proteins called Lhca's, surrounding the core of PSI. In total, the PSI-LHCI complex of higher plants contains 173 chlorophyll molecules, most of which are there to harvest sunlight energy and to transfer the created excitation energy to the reaction center (RC) where it is used for charge separation. The efficiency of the complex is based on the capacity to deliver this energy to the RC as fast as possible, to minimize energy losses. The performance of PSI in this respect is remarkable: on average it takes around 50 ps for the excitation to reach the RC in plants, without being quenched in the meantime. This means that the internal quantum efficiency is close to 100% which makes PSI the most efficient energy converter in nature. In this review, we describe the light-harvesting properties of the complex in relation to protein and pigment organization/composition, and we discuss the important parameters that assure its very high quantum efficiency. Excitation energy transfer and trapping in the core and/or Lhcas, as well as in the supercomplexes PSI-LHCI and PSI-LHCI-LHCII are described in detail with the aim of giving an overview of the functional behavior of these complexes.