Optical fibers are an excellent sensor platform. However, the detection and analysis of media outside the cladding and coating of standard fibers represent a long-standing challenge: light that is guided in the single optical core mode does not reach these media. Cladding modes help work around this difficulty, as their transverse profiles span the entire cross-section of the fiber cladding and reach its outer boundary. In this tutorial, we introduce and discuss in detail two recent advances in optical fiber sensors that make use of cladding modes. Both concepts share optomechanics as a common underlying theme. First, we describe a spatially continuous distributed analysis using the optical cladding modes of the fiber. Light is coupled to these modes using Brillouin dynamic gratings, which are index perturbations associated with acoustic waves in the core that are stimulated by light. Unlike permanent gratings, which are routinely used to couple light with cladding modes, Brillouin dynamic gratings may be switched on and off at will and can be confined to short fiber sections at arbitrary locations in a random-access manner. Second, we present the extension of the cladding mode sensor concept to include acoustic rather than optical modes. The acoustic cladding modes may be stimulated and monitored by guided light in the single core mode, and their linewidths are modified by the elastic properties of surrounding media. The principles and analyses of both concepts are provided in detail, alongside examples of experimental setups and results.