Dusty plasmas are electrically quasi-neutral media that, along with electrons, ions, neutral gas, radiation, and electric and/or magnetic fields, also contain solid or liquid particles with sizes ranging from a few nanometers to a few micrometers. These media can be found in many natural environments as well as in various laboratory setups and industrial applications. As a separate branch of plasma physics, the field of dusty plasma physics was born in the beginning of 1990s at the intersection of the interests of the communities investigating astrophysical and technological plasmas. An additional boost to the development of the field was given by the discovery of plasma crystals leading to a series of microgravity experiments of which the purpose was to investigate generic phenomena in condensed matter physics using strongly coupled complex (dusty) plasmas as model systems. Finally, the field has gained an increasing amount of attention due to its inevitable connection to the development of novel applications ranging from the synthesis of functional nanoparticles to nuclear fusion and from particle sensing and diagnostics to nano-contamination control. The purpose of the present perspectives paper is to identify promising new developments and research directions for the field. As such, dusty plasmas are considered in their entire variety: from classical low-pressure noble-gas dusty discharges to atmospheric pressure plasmas with aerosols and from rarefied astrophysical plasmas to dense plasmas in nuclear fusion devices. Both fundamental and application aspects are covered.