The Cloud evolved when there was worldwide recession and companies wanted to save money in data storage and computation. There are 3 main types of clouds if you will: PaaS, IaaS and SaaS in general.

Infrastructure as a Service is most intensive and heavy as far as power, stability and computing is concerned. It has to support the whole company model in the cloud. And of course multiple of them. Security in all kinds of computing is a huge challenge but then again cloud is very flexible and economic. There is always a debate on how the data and communications should be encrypted and managed. One of the challenges to the Cloud providers is power in their data center (where they have these huge servers , computers , storage, routers and switches). The data center is so huge that it consumes a massive scale of power. Power failure is not appreciable as it is supporting many companies at a time. The servers get so hot that new cooling system is required in the premises in addition to air conditioning. 

Within the Cloud there is a powerful software architecture, the most popular software around is : OpenStack among others (http://www.openstack.org/). It is an open source. It has many challenges of its own, like flexibility, security and privacy, availability, customization, performance, reliability, speed etc. You can actually contribute to it as it is open. There are also many legal issues that it needs to address as it is becoming  global and are being injected into new regions.

Cloud is being used in may different ways and researches are held everyday on how we can exploit it. one of recent research publications shows a remote computing can be done in the cloud. For example  a cyber physical system or a communication system may need some intensive computing which is expensive to bring back to the user location.

There is a challenge of inter-cloud communication that has generated financial and security risk. For example, communication between different cloud softwares like OpenStack, Hyper-V or V-sphere used by different cloud service companies have problems in communications. Please dig into manuscripts for details.

I think this will give you some insights. If you have specific questions on any specific area within cloud, please post.