We propose a new linear RGB-D simultaneous localization and mapping (SLAM) formulation by utilizing planar features of the structured environments. The key idea is to understand a given structured scene and exploit its structural regularities such as the Manhattan world. This understanding allows us to decouple the camera rotation by tracking structural regularities, which makes SLAM problems free from being highly nonlinear. Additionally, it provides a simple yet effective cue for representing planar features, which leads to a linear SLAM formulation. Given an accurate camera rotation, we jointly estimate the camera translation and planar landmarks in the global planar map using a linear Kalman filter. Our linear SLAM method, called L-SLAM, can understand not only the Manhattan world but the more general scenario of the Atlanta world, which consists of a vertical direction and a set of horizontal directions orthogonal to the vertical direction. To this end, we introduce a novel tracking-by-detection scheme that infers the underlying scene structure by Atlanta representation. With efficient Atlanta representation, we formulate a unified linear SLAM framework for structured environments. We evaluate L-SLAM on a synthetic dataset and RGB-D benchmarks, demonstrating comparable performance to other state-of-the-art SLAM methods without using expensive nonlinear optimization. We assess the accuracy of L-SLAM on a practical application of augmented reality.