Mathematical modeling is one of the fundamental techniques for understanding biophysical mechanisms in developmental biology. It helps researchers to analyze complex physiological processes and connect like a bridge between theoretical and experimental observations. Various groups of mathematical models have been studied to analyze these processes, and the nonlocal models are one of them. Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances (e.g., cell-cell, cell-tissue adhesions, neural networks, the spread of diseases, intra-specific competition, nanobeams, etc.). This review illustrates different nonlocal mathematical models applied to biology and life sciences. The major focus has been given to sources, developments, and applications of such models. Among other things, a systematic discussion has been provided for the conditions of pattern formations in biological systems of population dynamics. Special attention has also been given to nonlocal interactions on networks, network coupling and integration, including brain dynamics models that provide an important tool to understand neurodegenerative diseases better. In addition, we have discussed nonlocal modeling approaches for cancer stem cells and tumor cells that are widely applied in the cell migration processes, growth, and avascular tumors in any organ. Furthermore, the discussed nonlocal continuum models can go sufficiently smaller scales, including nanotechnology, where classical local models often fail to capture the complexities of nanoscale interactions, applied to build biosensors to sense biomaterial and its concentration. Piezoelectric and other smart materials are among them, and these devices are becoming increasingly important in the digital and physical world that is intrinsically interconnected with biological systems. Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue growth and shrinkage, and other areas increasingly important in biomedical and bioengineering applications. Finally, we provided a comprehensive summary of emerging trends and highlighted future directions in this rapidly expanding field.

The pursuit of artificial consciousness requires conceptual clarity to navigate its theoretical and empirical challenges. This paper introduces a composite, multilevel, and multidimensional model of consciousness as a heuristic framework to guide research in this field. Consciousness is treated as a complex phenomenon, with distinct constituents and dimensions that can be operationalized for study and for evaluating their replication. We argue that this model provides a balanced approach to artificial consciousness research by avoiding binary thinking (e.g., conscious vs. non-conscious) and offering a structured basis for testable hypotheses. To illustrate its utility, we focus on "awareness" as a case study, demonstrating how specific dimensions of consciousness can be pragmatically analyzed and targeted for potential artificial instantiation. By breaking down the conceptual intricacies of consciousness and aligning them with practical research goals, this paper lays the groundwork for a robust strategy to advance the scientific and technical understanding of artificial consciousness.