Micro- and nano-plastic (MP/NP) pollution represents a threat not only to marine organisms and ecosystems, but also a danger for humans. The effects of these small particles resulting from the fragmentation of waste of various types have been well documented in mammals, although the consequences of acute and chronic exposure are not fully known yet. In this review, we summarize the recent results related to effects of MPs/NPs in different species of fish, both saltwater and freshwater, including zebrafish, used as model organisms for the evaluation of human health risk posed by MNPs. The expectation is that discoveries made in the model will provide insight regarding the risks of plastic particle toxicity to human health, with a focus on the effect of long-term exposure at different levels of biological complexity in various tissues and organs, including the brain. The current scientific evidence shows that plastic particle toxicity depends not only on factors such as particle size, concentration, exposure time, shape, and polymer type, but also on co-factors, which make the issue extremely complex. We describe and discuss the possible entry pathways of these particles into the fish body, as well as their uptake mechanisms and bioaccumulation in different organs and the role of blood response (hematochemical and hematological parameters) as biomarkers of micro- and nano-plastic water pollution.