Supply chain management includes strategic, tactical, and operational decisions for long, medium, and short-term planning. Strategic decisions, such as network design, and operational decisions, such as last-mile routing, have mutual implications. Therefore, modelling them separately can lead to sub-optimal solutions. The integrated modelling of these decisions has been addressed as a location routing problem (LRP). This paper aims to identify the solution strategies and methods to solve the LRP, as well as related challenges and research opportunities based on a critical literature review. The findings reveal that 46% of the reviewed publications have adopted a multistage modelling approach to address the LRP, sequentially tackling strategic and operational decisions. Moreover, in addition to the challenge of modelling diverse decision levels, the LRP models need to incorporate variables such as time windows, delivery failure rates, demand density, etc. Five research opportunities are proposed: i) modelling the first and last mile with a strategic approach when making strategic network decisions, ii) integrating environmental and social objectives into the modelling framework, iii) applying the solution methods and algorithms to complex real-world cases, iv) exploring competitive and cooperative models in LRP, and v) evaluating the use of emerging technologies.