A bipartite quantum state is said to be steerable (from Alice's side) if the corresponding Einstein-Podolsky-Rosen steering experiment can be convincingly verified (from Alice's side). We show that the problem of determining the steerability of a bipartite quantum state can be stated as a nesting problem of convex objects in a linear space. Nesting criteria are then proposed. As the first application, we prove the conjecture on the steerability of T-states, confirming them as the first class of two-qubit states of lower symmetry than the Werner states of which the steerability can still be fully characterised. As the second application, we discuss our recent progress in understanding the long-standing question on the steerability of the Werner states beyond projective measurements.