Advanced functional materials have revolutionized our daily life and work in depth. Their applications are widely used in many fields, including but not limited to information technology, energy conversion and life science. However, the pace of improvement varies among different materials. For example, the trifecta of manufacturing, characterization, and theoretical understanding lays the foundation of Moore's law in the semiconductor industry, while the complex mechanisms reflected on coupled chemical, physical, and mechanical effects at the nanoscale evidently retard the progress of energy materials. Thus, a pressing as well as universal challenge facing development of advanced materials is how we can better understand their physics and various coupling at local length scales. Scanning Probe Microscopy (SPM) is a powerful tool to study a wide variety of physical properties at the nanoscale which can be directly traced to their microstructures and further linked to the performance on the device level. In this dissertation, we first introduce that SPM techniques have great potential to realize such promise by using halide perovskite solar cells as an example, which have emerged as one of the most promising next-generation photovoltaic materials. Yet their microscopic phenomena involving photo-carriers, ionic defects, spontaneous polarization are still inadequately understood. In this part, we highlight some recent progress and challenges of investigation toward local probing of its photocurrent, surface potential, spontaneous polarization, ionic motion, and chemical degradation via SPM. These findings resolve ambiguity regarding the crystalline nature of CH3NH3PbI3 and its implication on photovoltaic conversion, reconcile the diverse and apparent contradictory data reported in literature, and point a direction toward engineering ferroic domains for enhanced efficiency. We also summarize technical limitations and challenges encountered in this systematic study of CH3NH3PbI3 and emphasize the need of innovative experimental methodologies based on SPM to acquire high quality, efficient, and physically relevant scientific data for deep analysis. To enable such vision and handle those challenges, the recent advances in big data inspire us to head for a data-driven SPM. In this part, a rough piezoelectric material is first examined using SPM combined with our newly developed sequential excitation (SE) method, which acquires multi-dimensional data over a range of frequencies excited in a sequential manner and enables us to map its intrinsic electromechanical properties at the nanoscale with high fidelity. To pursue a faster scanning speed, we then upgrade SE to the high-throughput sequential excitation which can capture full-time contact dynamics of probe-sample interaction of all pixels in just one scan. Using electrochemically active granular ceria as an example, we map both linear and quadratic electrochemical strain accurately across grain boundaries with high spatial resolution where the conventional approach fails. Both damped harmonic oscillator (DHO) model and principal component analysis (PCA) are carried out to derive intrinsic electromechanical coupling of interests. It turns out that PCA can not only speeds up the analysis by four orders of magnitude, but also allows a physical interpretation of its modes in combination with the DHO model. This SE methodology can be easily adapted for other SPM modes to probe a wide range of microscopic phenomena. Finally, the collected big data can not only pave the way for materials research, but also repay the development of SPM techniques. Here we demonstrate an artificial intelligence scanning probe microscopy (AI-SPM) for pattern recognition and feature identification in ferroelectric materials and electrochemical systems. This data-driven AI-SPM can respond to classification via adaptive experimentation with additional probing at critical domain walls and grain boundaries, all in real-time on the fly without human interference. Key to our success is an efficient machine learning strategy based on a support vector machine (SVM) algorithm capable of pixel-by-pixel recognition instead of relying on data from full mapping, making real-time classification and control possible during scan, with which complex electromechanical couplings at the nanoscale in different material systems can be resolved by the AI. For SPM experiments that are often tedious, elusive, and heavily rely on human insight for execution and analysis, this is a major disruption in methodology. In conclusion, we believe such a data-driven SPM will not only facilitate the study of advanced functional materials, but also probably impact development for a wide range of scientific instruments.