Precision spectroscopy is a driving force for the development of our physical understanding. However, only few atomic and molecular systems of interest have been accessible for precision spectroscopy in the past, since they miss a suitable transition for laser cooling and internal state detection. This restriction can be overcome in trapped ions through quantum logic spectroscopy. Coherent laser manipulation originally developed in the context of quantum information processing with trapped ions allows us to combine the special spectroscopic properties of one ion species (spectroscopy ion) with the excellent control over another species (logic or cooling ion). The logic ion provides sympathetic cooling and is used to control and read out the internal state of the spectroscopy ion. In my presentation I will provide an overview of different implementations of quantum logic spectroscopy suitable for narrow (long-lived) and broad (dipole-allowed) transitions. Applications range from highly accurate optical clocks based on aluminium ions, over precision spectroscopy of broad and non-closed transitions in calcium isotopes, to non-destructive internal state detection and spectroscopy of molecular ions. Prospects to extend quantum logic spectroscopy to highly charged ions and first steps towards this goal will be discussed.Spectroscopy of these species enables a multitude of tests for physics beyond the Standard Model, such as probing for new force carriers and scalar fields that are dark matter candidates and could induce a variation of fundamental constants. Measurements of isotope shifts of narrow transitions in calcium isotopes probes nuclear structure and may allow to constrain new forces coupling electrons and neutrons. Precision spectroscopy of e.g. vibrational transitions in molecular ions will allow to put bounds on a possible variation of the electron-to-proton mass ratio, while highly charged ions are among the most sensitive systems to probe for a variation of the fine-structure constant.Picture: Sympathetically cooled highly-charged ions. Left: Ar13+ in a cloud of laser-cooled Be+ ions. Right: Two Be+ ions separated by a single Ar13+ ion.