The glaciers on the Antarctic Peninsula (AP) play an important role in ocean dynamics, global climate, and ecology. During recent decades, the AP has become an important contributor to sea-level rise. Despite this, the ice discharge, mass balance, and total volume of the region remain unclear. Furthermore, although the glaciers in the Antarctic periphery currently contribute modestly to sea-level rise, their contribution is projected to increase substantially until the end of the 21st century. This thesis aims to develop data processing and analysis methods that allow us to generate novel updated glacier data for the Antarctic Peninsula region. This is achieved using satellite remote sensing techniques such as radar and optical images, and also numerical models to infer the ice-thickness distribution of the Antarctic Peninsula Ice Sheet (APIS), with the goal of improving ice-discharge and total ice volume estimates for this region. The fundamentals of remote sensing are presented, including techniques such as synthetic aperture radar (SAR), InSAR, DInSAR, and offset-tracking. Optical imagery and Digital Elevation Model (DEM) techniques are also presented. We then focus on glacier flow modeling, describing the governing equations (mass and momentum conservation, rheology) and approximations such as shallow ice and perfect plasticity, used to infer the ice thickness of the Antarctic Peninsula Ice Sheet (APIS). The South Shetland Islands (SSI), located north of the Antarctic Peninsula, lack a geodetic mass balance calculation for the entire archipelago. Therefore, we estimate its geodetic mass balance over the period 2013-2017. Our estimation is based on remotely-sensed multispectral and interferometric SAR data covering 96% of the glacierized areas of the islands considered in our study and 73% of the total glacierized area of the SSI. Our results show a close to balance, slightly negative average specific mass balance for the whole area of −0.106 ± 0.007 m w.e. a⁻¹, and a mass change rate of −238 ± 12 Mt a⁻¹. These results are consistent with a wider scale geodetic mass balance estimation and with glaciological mass balance measurements at SSI locations for the same study period. They are also compatible with the cooling trend observed in the region between 1998 and the mid-2010s. We computed the ice discharge from the APIS north of 70ºS for the five most widely used ice-thickness reconstructions, using a common surface velocity field and a common set of flux gates. In this way, the differences in ice discharge can be solely attributed to the differences in ice thickness at the flux gates. The total volumetric ice discharge for 2015-2017 ranges within 45-141 km³ a⁻¹, depending on the ice-thickness model, with a mean of 87 ± 44 km³ a⁻¹. The substantial differences between the ice-discharge results and a multi-model normalized root-mean-squared deviation of 0.91 for the whole data set, reveal large differences and inconsistencies between the ice-thickness models. This makes evident the scarcity of appropriate ice-thickness measurements and the difficulty of the current models to reconstruct the ice-thickness distribution in this complex region. Motivated by this uncertainty about the ice-thickness distribution, we used a finite element method to infer the ice thickness in the APIS north of 70ºS applying a two-step approach. The first step uses two different assumptions, namely, the shallow ice approximation (SIA) and the perfect plasticity (PP). The second step then uses the mass conservation equation to estimate the thickness in fast-flowing regions, with the aim of overcoming the limitations of SIA and PP near the glacier termini. Manual adjustment of glacier outlines and new ways to deal with rheological parameters along the margins provided further improvements. The application of the model at our study site resulted in a total ice volume of 28.7 ± 6.8 103 km³ and an ice discharge of 95.0 ± 14.3 km³ a⁻¹.