In the short term I really think we are entering the era of accelerators. Accelerators like Micron's Automata Processor (1) for graph analysis, accelerators for compute intensive applications like Convolutional Neural Nets, continued innovation in DSPs, GPUs, etc.
Accelerators that can either outperform traditional processors or use significantly less power I think represent one of the major next steps after Moore's law. What comes next may well be a slime mold computer but I think at this point is pure speculation.
(1) - http://www.micronautomata.com - actually I heard about this on HN!