One important challenge for a set of agents to achieve more efficient collaboration is for these agents to maintain proper models of each other. An important aspect of these models of other agents is that they are often not provided, and hence must be learned from plan execution traces. As a result, these models of other agents are inherently partial and incomplete. Most existing agent models are based on action modeling and do not naturally allow for incompleteness. In this paper, we introduce a new and inherently incomplete modeling approach based on the representation of capabilities, which has several unique advantages. First, we show that the structures of capability models can be learned or easily specified, and both model structure and parameter learning are robust to high degrees of incompleteness in plan traces (e.g., with only start and end states partially observed). Furthermore, parameter learning can be performed efficiendy online via Bayesian learning. While high degrees of incompleteness in plan traces presents learning challenges for traditional (complete) models, capability models can still learn to extract useful information. As a result, capability models are useful in applications in which traditional models are difficult to obtain, or models must be learned from incomplete plan traces, e.g., robots learning human models from observations and interactions. Furthermore, we discuss using capability models for single agent planning, and then extend it to multi-agent planning (with each agent modeled separately by a capability model), in which the capability models of agents are used by a centralized planner. The limitation, however, is that the synthesized "plans" (called c-plans) are incomplete, i.e., there may or may not be a complete plan for a c-plan. This is, however, unavoidable for planning using partial and incomplete models (e.g., considering planning using action models learned from partial and noisy plan traces).