The global photovoltaic (PV) market is dominated by crystalline silicon (c-Si) based technologies with heavily doped, directly metallized contacts. Recombination of photo-generated 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 metallization. Strategies towards the implementation of passivating contacts in industrial environments are discussed.