When various vendors started to push the idea of using the cloud for computing infrastructure, the focus was on moving all your systems to a hosted solution. It didn't matter if you were interested in IaaS, SaaS, or PaaS solutions, there press from salespeople and even some technology professionals was for a complete migration. Put all your infrastructure in AWS, Azure, or some other place and your systems will run great.
Over time we've started to realize that moving to the cloud isn't as simple as just renting a new box or service and there may be plenty of work to get settled. Even then, there are some limitations or restrictions, either technical or otherwise that might make the cloud a poor choice. Security and compliance are often reasons to not move, but certainly there are also challenges with technology mismatches between on-premises and cloud platforms as well.
One of the very interesting things that I saw demonstrated a few years ago was the idea of the Azure Stack. The idea behind this technology is that a hybrid cloud can be built, with a single management view. Both the Azure cloud and local resources are combined together and managed as a single entity, with the choice of whether to run workloads on the vendor's infrastructure or your own on-premises machines. There are other versions of this, for example, with OpenStack working in conjunction with AWS.
There are many advantages to this, including the ability to limit certain workloads from bursting or moving from one environment to the other. One reason for this might be compliance. An organization might be required to keep some resources off of public networks, for example, the need to ensure that certain data is domiciled in a particular country. The reverse could also be true, with the desire to use a secure public portion of the Azure stack as their system might be certified in ways that your local infrastructure may not be.
I think the idea of cloud resources, managed, moved, and scaled as needed is a great one. It doesn't matter if this is all in your data center, all in the cloud, or both. Working this way allows a much more flexible use of any resource, wherever its located. Cutting edge organizations already do a small portion of this with ESX or Hyper-V hypervisors, software configured storage networks, or other software configured resources that can be reallocated on demand. Azure Stack, OpenStack, and other frameworks are a great way to start to leverage the cloud, but in a controlled manner that continues to use any capital investments you've made.