An important increase in the number of smart things, connected objects, smartphones, and sensors are founded every day, creating a huge amount of data called Big Data. Because of the dynamism of things and the limited capability of their resources and services to process and store this huge data, Cloud computing became an efficient, accessible, and reasonable solution. IoT in combination with Cloud functionalities provides a new phenomenon called the Cloud of Things (CoT) where many new possibilities are enabled. With the heterogeneity of different objects, the dynamism of their context, their distribution and the infinite cloud services, a middleware is a key solution. The main aim of this paper is to study middleware for self-adaptation of the Cloud of things environment into the context of objects. Toward this end, we first present some related features. Next, we compare some middlewares according to their characteristics. Then, we present some middlewares for static and dynamic adaptation and finally, we conclude this paper with a list of current challenges and issues in the design of a new middleware able to adapt dynamically and in execution time any cloud service into the context of the current object.