This thesis reports new analytical approaches involving the employment of various scanning probe microscopy techniques (along with other microscopy techniques), coupled -in particular- with numerical modelling to extract key information about surface properties and crystal dissolution. The set of techniques used include scanning electrochemical microscopy (SECM), scanning ion conductance microscopy (SICM), scanning electrochemical cell microscopy (SECCM), ion selective electrodes (ISEs), atomic force microscopy (AFM), and confocal laser scanning microscopy (CLSM). In general, the approaches involve the coupling of data from two techniques to enhance the amount of information that could be obtained in an experiment. A new bias modulated SICM technique is introduced as a powerful tool to map topography and surface charge density simultaneously. This significant advance takes SICM beyond its original use as a topographical technique and turns it into a method of greater scope and versatility. To further advance scanning electrochemical probe microscopy, the fabrication and application of dual function electrodes, coupling both SICM and SECM techniques is described. The SICM was used to map sample topography and for the local delivery of agents to the sample surface (here calcite microcrystals), while the SECM part was employed as an ion selective electrode to acquire ion activity profiles (Ca2+ and H+, respectively) in bulk solution and in proximity to the surface. The pH probe size was pushed down to the nanoscale, while the calcium ones were in the 1.5 - 3 μm across. A major aspect of this work was to analyse experimental measurements with numerical finite element method simulations enabling the determination of dissolution flux values, thus opening the door to many possible and interesting applications for these probes in the future. Acid attack on dental enamel surfaces is also considered using different approaches. In one approach SECM was coupled with CLSM to visualise the proton diffusion profile near enamel surfaces in a bid to extract highly temporal kinetic information about the acid attack on enamel. An attentive approach was to use the SECCM technique as a tool to probe acid-induced dissolution of enamel, by locally delivering protons with a well defined mass transport. Landing with the acidic droplet on the sample surface for different time periods generated etch pits, which were then analysed with AFM. A key aspect was to develop a numerical finite element method (FEM) model that was employed to extract dissolution kinetics for the different types of enamel samples (treated and untreated).