The global photovoltaic (PV) market is dominated by crystalline silicon (c-Si) based technologies with heavily doped, directly metallised contacts. Recombination of photogenerated electrons and holes at the contact regions is increasingly constraining the power conversion efficiencies of these devices as other performance-limiting energy losses are overcome. To move forward, c-Si PV technologies must implement alternative contacting approaches. Passivating contacts, which incorporate thin films within the contact structure that simultaneously supress recombination and promote charge carrier selectivity, are a promising next step for the mainstream c-Si PV industry. In this work we review the fundamental physical processes governing contact formation in c-Si. In doing so we identify the role passivating contacts play in increasing c-Si solar cell efficiencies beyond the limitations imposed by heavy doping and direct metallisation. Strategies towards the implementation of passivating contacts in industrial environments are discussed.