Physiology is a functional branch of the biological sciences, searching for general rules by which explanatory hypotheses are tested using experimental procedures, whereas palaeontology is a historical science dealing with the study of unique events where conclusions are drawn from congruence among independent lines of evidence. Vertebrate palaeophysiology bridges these disciplines by using experimental data obtained from extant organisms to infer physiological traits of extinct ones and to reconstruct how they evolved. The goal of this theme issue is to understand functional innovations imprinted on modern vertebrate clades, and how to infer (or ‘retrodict’) physiological capacities in their ancient relativesa posteriori.As such, the present collection of papers deals with different aspects of a rapidly growing field to understand innovations in: phospho-calcic metabolism, acid–base homeostasis, thermometabolism, respiratory physiology, skeletal growth, palaeopathophysiology, genome size and metabolic rate, and it concludes with a historical perspective. Sometimes, the two components (physiological mechanism and palaeobiological inference) are proposed in separate papers. Other times, the two components are integrated in a single paper. In all cases, the approach was comparative, framed in a phylogenetic context, and included rigorous statistical methods that account for evolutionary patterns and processes.This article is part of the theme issue ‘Vertebrate palaeophysiology’.