Branching Brownian motion is a random particle system which incorporates both the tree-like structure and the diffusion process. In this talk, we consider a slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motion with drift, undergo dyadic fission at a constant rate, and are killed upon hitting the origin. We are interested in the asymptotic behaviors of the process conditioned on survival up to a large time t as the process approaches criticality. Results like this are called Yaglom type results. Specifically, we will talk about the construction of the Yaglom limit law, Yaglom-type limits for the number of particles and the maximal displacement. Based on joint work with Julien Berestycki, Bastien Mallein and Jason Schweinsberg.