Networks-on-chips (NoCs) are an integral part of emerging manycore computing chips. They play a key role in facilitating communication among processing cores and between cores and memory. To meet the aggressive performance and energy-efficiency targets of machine learning and big data applications, NoCs have been evolving to leverage emerging paradigms such as silicon photonics and wireless communication. Increasingly, these NoC fabrics are becoming susceptible to security vulnerabilities, such as from hardware trojans that can snoop, corrupt, or disrupt information transfers on NoCs. This article surveys the landscape of security challenges and countermeasures across electronic, wireless, and photonic NoCs.