<p>When approximating a collection of eigenvalue-eigenvector pairs (eigenpairs) of a differential operator via finite element methods, the prevailing wisdom is that the finite element space should be well-suited to approximating the entire invariant subspace (the span of the eigenvectors), as opposed to just being well-suited to approximating some particular basis of this space. Over the past 15 years or so, there have been a variety of approaches proposed for achieving this goal as part of an adaptive algorithm. Each approach uses the current computed approximation of the eigenvector basis in some (sophisticated) way to estimate subspace approximation error and determine how to refine the current finite element space to improve the next approximation. When the collection of desired eigenpairs is large, these approaches become increasingly costly. We propose an alternative means of driving adaptive refinement, based on the solution of a single source problem—the so-called landscape function. After providing some theoretical and heuristic justification that "landscape refinement" is not an unreasonable proposition, we illustrate its practical performance on a variety of examples, primarily in the hp-adaptive setting, where we believe it provides an attractive alternative to current approaches.</p>