In the framework of the Cost Action CERTBOND (Reliable roadmap for certification of bonded primary structures), a wide group of researchers from 27 European Countries have had the opportunity to work on the topic of certification of bonded joints for primary structural applications from different engineering sectors such as the aerospace, automotive, civil engineering, wind energy and marine sectors. Since virtual testing and optimization are basic tools in the certification process, one of the key objectives of CERTBOND is to critically review some of the available models and failure theories for adhesive joints. The present paper summarizes the outcome of this task. Nine different models/theories are described in detail. Specifically, reviewed are the Classical Analytical Methods, the Process Zone Methods, Linear Elastic Fracture Mechanics (LEFM), the Virtual Crack Closure Technique (VCCT), the Stress Singularity Approach, Finite Fracture Mechanics (FFM), the Cohesive Zone Method (CZM), the Progressive Damage Modeling method and the Probabilistic methods. Also, at the end of the paper, the modeling of temperature effects on adhesive joints have been addressed. For each model/theory, information on the methodology, the required input, the main results, the advantages and disadvantages and the applications are given. © 2021 The Author(s).