Material degradations such as corrosion and erosion are prevalent in facilities of the energy sector. Excessive and unexpected material degradations can lead to catastrophic structure failures, severe service disruption and even loss of lives. Ultrasound-based non-destructive evaluation (NDE) and structural health monitoring (SHM) technology has been developed to provide quantitative data to monitor degradation processes so that they can be mitigated in the best possible way. This thesis aims to improve these ultrasound-based NDE and SHM methods by reducing their uncertainties and exploring their potential applications on emerging technologies. The first part of the thesis focuses on advancing temperature compensation strategies of the NDE and SHM technology. This is because environmental and operational conditions (EOCs), especially temperature changes are one of the biggest sources of uncertainties in the current ultrasonic measurements. At the same time, temperature controls the rate of various electrochemical processes and therefore influences the rate of material degradation. A novel dual-wave approach is presented to enhance the performance of the existing monitoring technology. By exciting both shear and longitudinal waves at the same location of a component, variations of component thickness and internal temperature distributions can be simultaneously monitored. It was shown that even under drastic thermal swings (40 celsius temperature change in under 3 minutes), thickness variations of 2 micrometers can be accurately tracked. Compared with the existing single-wave approach, thickness measurement errors can be reduced by a factor of 5. At the same time, ultrasonic temperature predictions agreed with the independent measurements using a resistance temperature detector (RTD) to within 2 celsius and corrosion-induced temperature prediction drift can be reduced by a factor of 9. The second part of the thesis explores the possibility of applying ultrasonic NDE and SHM technology on monitoring degradation phenomena in energy storage systems (ESS). ESS such as batteries have seen rapid developments recently due to the emerging demand to store energy produced from renewable resources. However, these devices also suffer from degradation issues and require appropriate monitoring solutions. This work targets a specific battery degradation phenomenon - dendrite growth at the electrode/electrolyte interface. A novel measurement method is proposed which can excite the SH0* mode guided wave in a waveguide that also serves as the battery electrode. Experimental investigations demonstrated the feasibility of the approach. The SH0* mode guided wave was shown to be sensitive to zinc dendrite in the order of tens of micrometres. Moreover, the results revealed correlations between ultrasonic signal variations and the underlying zinc plating/stripping processes, thus providing more physical insights into battery degradation mechanisms.