We present a technique-led review of the progression of precise radio astrometry, from the first demonstrations, half a century ago, until to date and into the future. We cover the developments that have been fundamental to allow high accuracy and precision astrometry to be regularly achieved. We review the opportunities provided by the next generation of instruments coming online, which are primarily: SKA, ngVLA, and pathfinders, along with EHT and other (sub)mm-wavelength arrays, Space-VLBI, Geodetic arrays, and optical astrometry from GAIA. From the historical development, we predict the future potential astrometric performance, and, therefore, the instrumental requirements that must be provided to deliver these. The next generation of methods will allow ultra-precise astrometry to be performed at a much wider range of frequencies (hundreds of MHz to hundreds of GHz). One of the key potentials is that astrometry will become generally applicable, and, therefore, unbiased large surveys can be performed. The next-generation methods are fundamental in allowing this. We review the small but growing number of major astrometric surveys in the radio, to highlight the scientific impact that such projects can provide. Based on these perspectives, the future of radio astrometry is bright. We foresee a revolution coming from: ultra-high-precision radio astrometry, large surveys of many objects, improved sky coverage, and at new frequency bands other than those available today. These will enable the addressing of a host of innovative open scientific questions in astrophysics.