Thanks to a rapid progress of high-power lasers since the birth of laser by T. H. Maiman in 1960, intense lasers have been developed mainly for studying the scientific feasibility of laser fusion. Inertial confinement fusion with an intense laser has attracted attention as a new future energy source after two oil crises in the 1970s and 1980s. From the beginning, the most challenging physics is known to be the hydrodynamic instability to realize the spherical implosion to achieve more than 1000 times the solid density. Many studies have been performed theoretically and experimentally on the hydrodynamic instability and resultant turbulent mixing of compressible fluids. During such activities in the laboratory, the explosion of supernova SN1987A was observed in the sky on 23 February 1987. The X-ray satellites have revealed that the hydrodynamic instability is a key issue to understand the physics of supernova explosion. After collaboration between laser plasma researchers and astrophysicists, the laboratory astrophysics with intense lasers was proposed and promoted around the end of the 1990s. The original subject was mainly related to hydrodynamic instabilities. However, after two decades of laboratory astrophysics research, we can now find a diversity of research topics. It has been demonstrated theoretically and experimentally that a variety of nonlinear physics of collisionless plasmas can be studied in laser ablation plasmas in the last decade. In the present paper, we shed light on the recent 10 topics studied intensively in laboratory experiments. A brief review is given by citing recent papers. Then, modeling cosmic-ray acceleration with lasers is reviewed in a following session as a special topic to be the future main topic in laboratory astrophysics research.