Although recent advances in the field of robotics have greatly increased robotic capabilities for several applications, autonomous robots are still in their infancy regarding their support of onsite construction. Unlike production robots that are used, for instance, in automotive industries, autonomous robotic systems should be designed with special considerations, such as the complexity of the cluttered and dynamic working space, inaccuracy in positioning because of the nature of mobile systems, and so forth. Thus, construction has been known as a highly complex application field for robotic systems, especially in unknown environments. In this thesis, we focus on the developments of an autonomous construction system by taking inspiration from architectural designs found in the animal kingdom. The construction system allows robots to build functional structures over a different range of environmental conditions or in unknown sites without the use of any predefined construction plan (i.e., blueprint). We call this approach adaptive and functional autonomous construction (AFAC). Indeed, AFAC is a robust and intelligent system that can tackle unforeseen problems of unknown environments and faults made during the course of building. We present two approaches for AFAC. One is a local approach that enables robots to locally sense features of their environment and then act immediately according to defined rules without using any global representation or knowledge of the world. Second is a global approach, which involves building structures by analysing global representations and knowledge produced by the robots. This approach consists of three phases: the first phase is exploration, to map the unknown environment and to find important elements. In the second phase, an effective construction plan is autonomously computed using collected data and the defined functions. Finally, in the last phase, the robot builds structures based on the computed construction plan. One interesting implementation of the introduced construction system is its potential use in a post disaster environment, where an autonomous robotic system can perform construction tasks in the rescue operation. Robots can be employed to build protective structures for rescue functions, including stabilizing large structures or protecting victims in unknown environments, where the environment are perhaps covered by debris. Inasmuch as the robots cannot plan in advance to build these structures, the rescue application is a well suited case for the study and implementation of AFAC in unknown and cluttered environments. Through implementation of AFAC in the rescue situations, we develop AFAC from scratch to the level at which the robots can autonomously apply AFAC's principles for use in the new classes of construction applications. We also study and compare the local and global approaches of AFAC. In addition, we develop new exploration methods and construction plan computation methodologies for the global approach to efficiently lead AFAC.