This paper analyzes the concept of cloud computing. More specifically, it deals with developing applications in the cloud on the Windows Azure platform. Initially it defines the current view of cloud computing and examines trends and circumstances enabling the shift to the cloud. The paper shows that when historic context, paradigms and technology are analyzed, it becomes apparent that the idea of cloud computing rests on already familiar concepts – virtualization, mainframe computers, distributed systems etc. The majority of these concepts have been developed in the 60s and 70s in IBM laboratories. The paper also examines the basic characteristics of cloud computing which inform the current view of computing. Based on these characteristics, basic models of cloud computing and challenges arising from the use and implementations of such services are explained. What follows is an analysis of Windows Azure as a platform for application development which serves to demonstrate basic premises on which the Windows Azure service is built. There is also an overview of available resources. Individual services are presented from an economic viewpoint as well. Finally, there is a description of a simple application demonstrating some basic concepts and services of the Windows Azure system. A simple application was developed in order to showcase some key platform attributes, such as simple development, setting applications in the cloud, scaling and managing by using Windows Azure building blocks.