Large-scale neuronal networks and their complex distributed microcircuits are essential to generate perception, cognition, and behavior that emerge from patterns of spatiotemporal neuronal activity. These dynamic patterns emerging from functional groups of interconnected neuronal ensembles facilitate precise computations for processing and coding multiscale neural information, thereby driving higher brain functions. To probe the computational principles of neural dynamics underlying this complexity and investigate the multiscale impact of biological processes in health and disease, large-scale simultaneous recordings have become instrumental. Here, a high-density microelectrode array (HD-MEA) is employed to study two modalities of neural dynamics - hippocampal and olfactory bulb circuits from ex-vivo mouse brain slices and neuronal networks from in-vitro cell cultures of human induced pluripotent stem cells (iPSCs). The HD-MEA platform, with 4096 microelectrodes, enables non-invasive, multi-site, label-free recordings of extracellular firing patterns from thousands of neuronal ensembles simultaneously at high spatiotemporal resolution. This approach allows the characterization of several electrophysiological network-wide features, including single/-multi-unit spiking activity patterns and local field potential oscillations. To scrutinize these multidimensional neural data, we have developed several computational tools incorporating machine learning algorithms, automatic event detection and classification, graph theory, and other advanced analyses. By supplementing these computational pipelines with this platform, we provide a methodology for studying the large, multiscale, and multimodal dynamics from cell assemblies to networks. This can potentially advance our understanding of complex brain functions and cognitive processes in health and disease. Commitment to open science and insights into large-scale computational neural dynamics could enhance brain-inspired modeling, neuromorphic computing, and neural learning algorithms. Furthermore, understanding the underlying mechanisms of impaired large-scale neural computations and their interconnected microcircuit dynamics could lead to the identification of specific biomarkers, paving the way for more accurate diagnostic tools and targeted therapies for neurological disorders.