This dissertation presents a study of multimode polymer waveguide technology for use in board-level communication links for future data centres and supercomputers. The motivation for this work comes from the severe interconnection bandwidth challenges faced by the conventional electrical interconnections technology and the potential performance advantages of optical interconnections. This thesis presents the work to address the bandwidth bottleneck by developing high-bandwidth multimode polymer waveguides. The use of multimode waveguides provides relaxed alignment tolerances enabling low-cost assembly tools. Siloxane polymer materials developed by Dow Corning Corporation are chosen to form the waveguides in this work due to their favourable optical properties (optical losses as low as 0.03 dB/cm and the ability to withstand temperatures in excess of 350 °C) that allow the waveguides to be directly integrated on printed circuits boards (PCBs) using conventional manufacturing processes. Useful design rules for the use of the multimode polymer waveguides are theoretically derived while the bandwidth-length products are investigated under various launch conditions. Frequency-domain measurements and ultra-short pulse measurements are then carried out to investigate the bandwidth performance of the polymer waveguides under different launch conditions and with lateral misalignments. The instrument-limited frequency-domain measurements show that these waveguides exhibit bandwidth-length products (BLPs) of at least 35 GHz×m, while the pulse broadening measurements reveal the actual BLPs to be in excess of 70 GHz×m under a 50 μm multimode-fibre (MMF) launch and 100 GHz×m for a restricted launch across a wide range of input offsets (>±10 μm). This shows the potential for data transmission rates of 100 Gb/s and beyond over a single waveguide channel. A theoretical model is developed using the measured refractive index profile and good agreement with the above experimental results is found. The effects of graded refractive index profiles on the performance of waveguide components (bends, crossings) are also investigated, demonstrating that appropriate refractive index engineering can provide enhanced waveguide loss performance while exhibiting adequate bandwidth. Waveguide bends with excess loss below 1 dB for a radius >6 mm, crossings with loss less than 0.02 dB/crossing while exhibiting adequate link bandwidth (>47 GHz×m) can be achieved for a MMF launch. On this basis, advanced modulation formats are investigated across the board-level waveguide links for further increasing the on-board data rates. Record NRZ-based 40 Gb/s and 56 Gb/s PAM-4 based data transmission over a 1 m long multimode polymer spiral waveguide are theoretically and experimentally demonstrated.