For more than a century, chromatography has been indispensable as a separation method for both analytics and purification. Among the variety of chromatographic techniques, liquid chromatography has a special status owing to its efficiency and versatility, and its status is further enhanced by the continuous improvements of analysers, materials, methods and understanding, all supported by computational approaches. High performance liquid chromatography (HPLC) has always held a special place in pharmaceutical processing, and computational HPLC has been explored since the very early stages of computing, although without having yet reached its full potential. Herein, we provide a comprehensive and critical review of recent developments in designing and operating liquid chromatographic systems, focussing on their modelling approaches and control strategies at large scale.