New perspectives have been opened up in the field, of laser-matter interactions due to recent advances in laser technology, leading to laser systems of high contrast and extreme intensity values, where the frontier of maximum intensity is pushed now to about 10²² W/cm². Many striking phenomena such as laser-acceleration of electrons up to the GeV level, fast moving ions with kinetic energies of several 10s of MeV, as well as nuclear physics experiments have already actuated a broad variety of theoretical as well as experimental studies. Also highly relativistic effects like laser induced electron-positron pair production are under discussion. All these activities have considerably stimulated the progress in understanding the underlying physical processes and possible applications. This article reviews recent advances in the experimental techniques as well as the associated plasma dynamics studies at relativistic intensities performed at the Max-Born-Institute (MBI). Interactions of a laser pulse at intensities above 10¹⁹ W/cm² with water- and heavy-water droplets, as well as, with thin foils are discussed. Rear and front side acceleration mechanisms, particle dynamics inside the dense target, proton source characteristics, strong modulations in proton and deuteron emission spectra, and finally generation of quasi-monoenergetic deuteron bursts are the topics covered in the article.