In this thesis, I discuss the fabrication and measurement of Al/AlOx/Al transmons that have electrodes with different superconducting gaps. With gap-engineering, the tunneling of single quasiparticle from the low-gap side to the high-gap side can be suppressed, hence increasing the relaxation time T1. The best gap-engineered device showed T1 exceeding 300 μs. Large T1 fluctuations in my devices were also observed. I proposed a mechanism for exploring the T1 fluctuation data and discuss the possible underlying cause of the T1 fluctuations. I first discuss the theory of the loss in gap-engineered transmons, with a focus on the loss from non-equilibrium quasiparticles. The model yields the quasiparticle-induced loss in transmons and its dependence on temperature. I also discuss how multiple Andreev reflection (MAR) effects might alter these conclusions, leading to a further reduction in T1. I then describe the design, fabrication and basic characterization of the transmon chip SKD102, which features two transmons – one with thin-film electrodes of pure Al and another that had one electrode made from oxygen-doped Al. I next examined T1 vs temperature and how the T1 fluctuations depended on temperature. I compare my results to a simple model and find reasonable agreement in transmons on chip SKD102, KL103 and KL109, which had different electrode and layer configurations. Finally, I analyze T1 fluctuations in different devices and as a function of temperature and propose a model to explain this behavior. Over the different devices, the T1 fluctuation magnitude roughly scaled as T13/2. With increasing temperature, T1 decreases due to a higher density of thermally generated quasiparticles. In contrast, for an individual device measured from 20mK to 250 mK, the fluctuation magnitude appears to be proportional to T1. I present a model of quasiparticle dissipation channels that reproduces both of these observed scaling relationships.