The paper presents the ‘progressive review’ for high pressure preservation/processing (HPP) (cold pasteurization) of foods and the next-generation high-pressure and high temperature (HPHT, HPT) food sterilization technologies. It recalls the basics of HPP and HPT, showing their key features and advantages. It does not repeat detailed results regarding HPP and HPT implementations for specific foods, available in numerous excellent review papers. This report focuses on HPP and HPT-related issues that remain challenging and can hinder further progress. For HPP implementations, the reliable modeling of microorganisms’ number decay after different times of high pressure treatment or product storage is essential. This report indicates significant problems with model equations standard nonlinear fitting paradigm and introduces the distortion-sensitive routine enabling the ultimate validation. An innovative concept based on the barocaloric effect is proposed for the new generation of HPT technology. The required high temperature appears only for a strictly defined short time period controlled by the maximal pressure value. Results of the feasibility test using neopentyl glycol as the barocaloric medium are presented. Attention is also paid to feedback interactions between socioeconomic and technological issues in the ongoing Industrial Revolution epoch. It indicates economic constraints for HPP and HPT developments and emerging business possibilities. The discussion recalls the inherent feedback interactions between technological and socioeconomic innovations as the driving force for the Industrial Revolution epoch.