The methods described in Jean Meeus's book are still valid, and accurate enough for the needs of most amateur and many professional astronomers. The science of positional astronomy doesn't change so rapidly that a book published in 1991 would be out of date only 30 years later. Even methods developed in the 19th century, such as Besselian elements of eclipses, are still useful in the 21st century.
Having said that, better solar system ephemerides do appear from time to time, such as the newer ones from IMCCE which supersede VSOP87. In my own code (written in Java and available at GitHub: https://github.com/DavidHarper/astrojava) I prefer to use the JPL Development Ephemeris representations of the orbits of the Moon and planets, because they are computationally easier to use than the IMCCE representations. However, I don't criticise Meeus (or anyone else) for choosing VSOP87.