This article presents a comprehensive critical overview of fundamental and practical aspects of the modern stripline broadband ferromagnetic resonance (BFMR) spectroscopy largely employed for the characterisation of magnetic low-dimensional systems, such as thin ferro-and ferromagnetic, multiferroic and half-metallic films, multi-layers and nanostructures. These planar materials form the platform of the nascent fields of magnonics and spintronics. Experimental and theoretical results of research on these materials are summarised, along with systematic description of various phenomena associated with the peculiarities of the stripline BFMR, such as the geometry of stripline transducers, the orientation of the static magnetic field, the presence of microwave eddy currents, and the impacts of non-magnetic layers, interfaces and surfaces in the samples. Results from more than 240 articles, textbooks and technical reports are presented and many practical examples are discussed in detail. This review will be of interest to both general physical audience and specialists conducting research on various aspects of magnetisation dynamics and nanomagnetism.