Spin waves are the elementary excitations of the spin system in a magnetically ordered material state and magnons are their quasi particles. In the following article, we will discuss Brillouin light scattering (BLS) spectroscopy which is now a well-established tool for the characterization of spin waves. BLS is the inelastic scattering of light from spin waves and confers several benefits: the ability to map the spin-wave intensity with spatial resolution and high sensitivity as well as the potential for the simultaneous detection of frequency and wave vector. For several decades, the field of spin waves gained huge interest by the scientific community due to its relevance regarding fundamental issues in spin dynamics. Recently, the ongoing research in the field of magnonics has put particular emphasis on the high potential of spin waves regarding information technology. Opposed to charge-based schemes in conventional electronics and spintronics, magnons are charge-free currents of angular momentum, and, therefore, less subject to dissipative scattering processes. These ideas have propelled the quest for concepts to guide and manipulate spin-wave transport as well as for the miniaturization of spin-wave conduits towards sub-micrometer dimensions. For the further development of potential spin-wave-based devices, the ability to directly observe spin-wave propagation with spatial resolution is crucial. As an optical technique, BLS allows for a sub-micron space resolution by the implementation of a microscope objective in the optical setup. Over the last decade, this micro-focus BLS technique has become an established method for the investigation of spin waves in microstructured magnetic elements and proved its value in particular regarding magnonics. In this article, we will discuss the basic principles of BLS and illustrate the experimental optical setup. Particular emphasis will be put on the implementation of the high spatial resolution of BLS microscopes as well as on their computer based operation and automated sample positioning. Owing to these improvements in ease of use as well as experimental applicability, the BLS technique has maintained its relevance for investigations on spin waves in miniaturized magnetic structures as will be illustrated by a selection of experiments.