The use of concrete-filled tubular composite members and composite beams has been implemented in many structural systems due to their robust structural performance, constructability, and inherent synergy when the steel and concrete components are properly designed and detailed together. While extensive research has been conducted on concrete-filled steel structural members, relatively little has been done regarding similar composite connections. Understanding how composite connections behave in structures and how they should be modeled during the design process is crucial to predict the actual structural behavior of these types of elements when subjected to different loading conditions. The goal of this research is to numerically evaluate CFTs or SRCs members and their connections subjected to axial, shear, and flexural load. Predicting composite connection behavior is exceptionally challenging due to the coupled behavior of the steel and concrete, the residual stresses in the steel, local buckling of the connection, and the sensitivity of the stress-strain response to the steel-concrete contact and confinement performance. To address these issues, a thorough literature search has been carried out and a state-of-the-art report on experimental and numerical models for composite connections is presented. The selected tests represent a range of geometries, materials, and governing failure modes. Initially, a generic connection modeling process was developed and calibrated against a classical test, then three more connections were modeled. To further the understanding of composite behavior, shear studs in steel-concrete composite beams were modeled next, taking as reference a recent experimental program that resulted in an unusual failure. Results indicate that the model can reproduce the most important behavioral aspects observed in the tests, tracking well the strength and stiffness of the samples up to ultimate. The load-deformation curves of the experimental specimens and the analytical models show very good agreement in their transitions and indicate that the behavior of the composite joints is controlled mainly by both the strength of the concrete and the confining effect of the steel tube in the joint. A data appendix containing 135 tests is described and the main characteristics of these tests are summarized in the text.