The main objectives pursued by parallelism in communications are network capacity enhancement and fault-tolerance. Efficiently enhancing the capacity of a network by parallel communications is a non-trivial task. Some applications may also allow one to split the sources and destinations into multiple sources and destinations. An example is parallel Input/Output (I/O). Parallel I/O requires scalability, high throughput and good load balance. Low granularity enables good load balance but tends to reduce throughput. In this thesis we combine fine granularity with scalable high throughput. The network overhead can be reduced and the network throughput can be increased by aggregation of data into large messages. Parallel transmissions from multiple sources to multiple destinations traverse the network through many different paths which have numerous intersections in the network. In low latency high performance networks, serious congestions occur due to large indivisible messages competing for shared resources. We propose to optimally schedule parallel communications by taking into account the network topology. The developed liquid scheduling method optimally uses the potential transmission capacity of a network. Fault-tolerance is typically achieved by maintaining backup communication resources, which are kept idle as long as the primary resource is operational. A challenging idea, inspired by nature, is to simultaneously use all parallel resources. This idea is applied to fine-grained packetized communications. It also relies on erasure resilient codes for combating network failures.