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The paper reviews methods that seek to draw causal inference from observational data and demonstrates how they can be applied to empirical problems in engineering research. It presents a framework for causal identification based on the concept of potential outcomes and reviews core contemporary methods that can be used to estimate causal quantities. The paper has two aims: first, to provide a consolidated overview of the statistical literature on causal inference for the data centric engineering community; and second, to illustrate how causal concepts and methods can be applied. The latter aim is achieved through Monte Carlo simulations designed to replicate typical empirical problems encountered in engineering research. R code for the simulations is made available for readers to run and adapt and citations are given to real world studies. Causal inference aims to quantify effects that occur due to explicit intervention (or 'treatment') in non-experimental settings, typically for non-randomly assigned treatments. The paper argues that analyses of engineering interventions are often characterized by such conditions, and consequently, that causal inference has immediate and valuable applicability.