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This paper investigates degradation modeling under dynamic conditions and its applications. Both univariate and multiple competing degradation processes are considered with individual degradation paths being described by Wiener processes. Parametric and non-parametric approaches are used to capture the effect of environmental conditions on process parameters. For competing degradation processes, we obtain the probability that a particular process reaches a pre-defined threshold, before other processes, over future time intervals. In particular, we consider the potential statistical dependence among the latent remaining lifetimes of multiple degradation processes due to unobserved future environmental factors. Two case studies, aircraft piston pump wear and US highway performance deterioration, are presented. Comprehensive comparison studies are also performed to generate some critical insights on the proposed approach. Data have been made available on GitHub.