Background: Genetic influences are ubiquitous as virtually all phenotypes and most exposures typically classified as environmental have been found to be heritable. A polygenic score summarises the associations between millions of genetic variants and an outcome in a single value for each individual. Ever lowering costs have enabled the genotyping of many samples relevant to child psychology and psychiatry research, including cohort studies, leading to the proliferation of polygenic score studies. It is tempting to assume that associations detected between polygenic scores and phenotypes in those studies only reflect genetic effects. However, such associations can reflect many pathways (e.g. via environmental mediation) and biases. Methods: Here, we provide a comprehensive overview of the many reasons why associations between polygenic scores, environmental exposures, and phenotypes exist. We include formal representations of common analyses in polygenic score studies using structural equation modelling. We derive biases, provide illustrative empirical examples and, when possible, mention steps that can be taken to alleviate those biases. Results: Structural equation models and derivations show the many complexities arising from jointly modelling polygenic scores with environmental exposures and phenotypes. Counter-intuitive examples include that: (a) associations between polygenic scores and phenotypes may exist even in the absence of direct genetic effects; (b) associations between child polygenic scores and environmental exposures can exist in the absence of evocative/active gene-environment correlations; and (c) adjusting an exposure-outcome association for a polygenic score can increase rather than decrease bias. Conclusions: Strikingly, using polygenic scores may, in some cases, lead to more bias than not using them. Appropriately conducting and interpreting polygenic score studies thus requires researchers in child psychology and psychiatry and beyond to be versed in both epidemiological and genetic methods or build on interdisciplinary collaborations.