Internet of Things (IoT) is presenting an enormous growing, in numbers, it is estimated that over 50 billion of devices will be connected to Internet by 2020. Therefore, it presents a high scalability requirement to manage every resource connected to the network. Therefore, It is required a high capability for autonomous registration and discovery of resources and services. In addition, it should be dynamically adapted with the inclusion of new devices in the network and changes of the existing ones. Nowadays, the most extended discovery architecture for the Internet is the Domain Name Systems (DNS), which is offering through the extensions multicast DNS (mDNS) and DNS Service Directory (DNS-SD) the query and discovery of services by type and properties. It has been already carried out some initial works on mDNS and DNS-SD for the discovery of things. Thereby, it can satisfy the discovery of resources from the IoT point of view, and discovery of services, i.e. Web Services such as CoAP from the Web of Things point of view. But, it has not been yet analyzed the impact of DNS for Smart Objects, since it cannot be directly applied, because these protocols are designed for host-based requirements, where they are not taking into account the design issues and constraints from the Smart Objects. For that reason, this paper analyzes the requirements and design issues to apply these discovery techniques in Smart Objects, carries out an overview of the satisfaction of them in the initial solutions for IoT, in order to finally offer an evaluation of different ways to apply mDNS and DNS-SD for Smart Objects, concluding with a set of recommendations and lessons learned to build a lightweight implementation of mDNS and DNS-SD for resource discovery and directory.