The agreements that determine whether material can lawfully be used to train a model. Increasingly this is a commercial negotiation rather than an assumption, with news organisations, image libraries and forums signing paid deals. For anyone building on top of a model, the equivalent question is whether the licence allows you to use the outputs the way you intend.
Technical view
Three layers need checking separately: the licence on training data, the licence on model weights, and the terms of service governing outputs and their reuse in further training. Open-weight releases frequently carry bespoke licences with acceptable-use clauses or commercial thresholds and are not open source in the recognised sense. Provenance tracking of training data is becoming a compliance expectation rather than a courtesy, and it is very difficult to add retrospectively.
Related
Part of AI Terminology Index, section: Data.