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Remote sensing observations meet some limitations when used to study the bulk atmospheric composition of the giant planets of our solar system. A remarkable example of the superiority of in situ probe measurements is illustrated by the exploration of Jupiter where key measurements such as the determination of the noble gases abundances and the precise measurement of the helium mixing ratio have only been made available through in situ measurements by the Galileo probe. This paper describes the main scientific goals to be addressed by the future in situ exploration of Saturn placing the Galileo probe exploration of Jupiter in a broader context and before the future probe exploration of the more remote ice giants. In situ exploration of Saturn's atmosphere addresses two broad themes that are discussed throughout this paper: first the formation history of our solar system and second the processes at play in planetary atmospheres. In this context we detail the reasons why measurements of Saturn's bulk elemental and isotopic composition would place important constraints on the volatile reservoirs in the protosolar nebula. We also show that the in situ measurement of CO (or any other disequilibrium species that is depleted by reaction with water) in Saturn's upper troposphere would constrain its bulk O/H ratio. We highlight the key measurements required to distinguish competing theories to shed light on giant planet formation as a common process in planetary systems with potential applications to most extrasolar systems. In situ measurements of Saturn's stratospheric and tropospheric dynamics chemistry and cloud forming processes will provide access to phenomena unreachable to remote sensing studies. Different mission architectures are envisaged which would benefit from strong international collaborations.