The PCI Express 4.0 specification will enable bandwidth of up 64GB/s, double as much as what's offered by the seven-year old PCI Express 3.0 specification. There was a long delay between the introduction of PCI Express 3.0 and PCI Express 4.0 but PCI-SIG is speeding things up by planning a rollout of PCI Express 5.0 in 2019. That specification will double the bandwidth once more to 128GB/s.
PCI-SIG promises it will ratify the final PCI Express 4.0 specification by the end of 2017, but several vendors are already offering 16GT/s controllers based on the 0.9 revision of the specification. PCI Express 4.0 will be short lived as PCI Express 5.0 is already on revision 0.3 and is on track to hit 0.5 by Q4 2017.
When these innovations will seep through to the consumer market remains a mystery. Tom's Hardware writes AMD isn't planning to support PCI Expres 4.0 until 2020. There's been no indication when Intel plans to support it:
The PCI-SIG defines the specification, but it has no control over when the end devices make it to market. Intel and AMD are the key enablers for the broad desktop market; we certainly won't see PCIe 4.0 GPUs and SSDs without a slot to plug them into. AMD has slated PCIe 4.0 for 2020. We imagine Intel is also chomping at the bit to deploy PCIe 4.0 3D XPoint and NVMe SSDs, but the company remains silent on its timeline.