Industry 4.0 represents a new industrial revolution that will dramatically change the landscape in many sectors, including manufacturing and logistics. Robotics, machine intelligence, and new forms of connectivity are key ingredients of this paradigm. 5G mobile networks are expected to play a crucial role, supporting a lower cost per transported bit in air and a lower latency compared with 4G. 5G radio ensures different performance levels in very heterogeneous coverage situations, including a mix of indoor and outdoor contexts. Mobile network evolution requires new transport networks to address the new challenging requirements: increasing transmission capacity, compatibility with latency-critical applications, significantly reduced cost with respect to conventional metro network segments, lower energy consumption, and, in some cases, switching capabilities. Optical communications and networking will play a key role in these new transport scenarios, where tailored transmission techniques and network architectures are needed. This paper discusses the requirements and challenges that Industry 4.0 scenarios pose to optical communications and networking architectures. Performance of optical transmission schemes, tailored to support these new radio access networks, are detailed and benchmarked. A network test bed, focused on transport for vertical use cases, is described. Experimental results demonstrate the compliance of the proposed optical transport network with a latency-critical cloud robotics application, which presents industry-grade connectivity needs.