Dual quaternions, in particular, unit dual quaternions, have found wide applications in robotics, 3D motion modelling and control, and computer graphics. Some very important engineering problems, such as the formation control of UAV (unmanned aerial vehicles) and small satellites are now based upon dual quaternions. In the past two years, my collaborators and I have explored dual quaternions and dual quaternion matrices as well as their applications in formation control, hand-eye calibration and simultaneous location and mapping (SLAM). In this talk, I will report our results in dual quaternions and dual quaternion matrices in the past two years.