Observational non-randomized clinical trials comparing two treatments longitudinally on efficacy and safety outcomes for a given indication are not uncommon, especially in the post-marketing setting. Often, such trials are called registries, where patients are not randomly assigned to receive treatments of interest but rather where treatments are assigned at the discretion of the patient and treating physician. Further, some pre-market clinical trials and registries are “single arm”, where all enrolled patients are administered only the experimental treatment and followed longitudinally for outcomes. Data collected from such single-arm trials are often compared to outcomes collected from untreated patients who were followed in a “natural history” study. This approach is especially common in trials of rare diseases, where all patients receive the experimental treatment in a pre-market trial since the desire is to maximize the number of subjects receiving the experimental treatment. The challenges to comparing two treatment groups in a non-randomized two-treatment registry, and the challenges to comparing treated to untreated patients in a single-arm vs. natural history setting, are common and numerous and include accounting for the facts that groups being compared may differ on (a) distribution of baseline demographic characteristics; (b) standard medical care practices due to not being followed contemporaneously; and (c) post-baseline characteristics such as different follow-up schedules, especially in natural history and registry studies. Here, we discuss approaches, including covariate adjustment and matching, that have been used to address these issues in the above settings for continuous, dichotomous and time-to-event outcomes, using real-life examples. The challenges, advantages and disadvantages of various approaches are discussed, as are the sensitivity analyses used to assess robustness of results.