Deep learning shows excellent performance usually at the expense of heavy computation. Recently, model compression has become a popular way of reducing the computation. Compression can be achieved using knowledge distillation or filter pruning. Knowledge distillation improves the accuracy of a lightweight network, while filter pruning removes redundant architecture in a cumbersome network. They are two different ways of achieving model compression, but few methods simultaneously consider both of them. In this paper, we revisit model compression and define two attributes of a model: distillability and sparsability, which reflect how much useful knowledge can be distilled and how many pruned ratios can be obtained, respectively. Guided by our observations and considering both accuracy and model size, a dynamically distillability-and-sparsability learning framework (DDSL) is introduced for model compression. DDSL consists of teacher, student and dean. Knowledge is distilled from the teacher to guide the student. The dean controls the training process by dynamically adjusting the distillation supervision and the sparsity supervision in a meta-learning framework. An alternating direction method of multiplier (ADMM)-based knowledge distillation-with-pruning (KDP) joint optimization algorithm is proposed to train the model. Extensive experimental results show that DDSL outperforms 24 state-of-the-art methods, including both knowledge distillation and filter pruning methods.