Every time you send a prompt to a model you actually send the entire previous conversation along with it, in an array that looks like this:

  curl https://api.anthropic.com/v1/messages \
    -H "content-type: application/json" \
    -H "x-api-key: $(llm keys get anthropic)" \
    -H "anthropic-version: 2023-06-01" \
    -d '{
      "model": "claude-haiku-4-5-20251001",
      "max_tokens": 1024,
      "messages": [
        {
          "role": "user",
          "content": "What is the capital of France?"
        },
        {
          "role": "assistant",
          "content": "The capital of France is Paris."
        },
        {
          "role": "user",
          "content": "Germany?"
        },
        {
          "role": "assistant",
          "content": "The capital of Germany is Berlin."
        },
        {
          "role": "user",
          "content": "Belgium?"
        }
      ]
    }'
  

You can see this yourself if you use their APIs.