  Large Language Models (LLMs) are revolutionizing several areas of Artificial
Intelligence. One of the most remarkable applications is creative writing,
e.g., poetry or storytelling: the generated outputs are often of astonishing
quality. However, a natural question arises: can LLMs be really considered
creative? In this article we firstly analyze the development of LLMs under the
lens of creativity theories, investigating the key open questions and
challenges. In particular, we focus our discussion around the dimensions of
value, novelty and surprise as proposed by Margaret Boden in her work. Then, we
consider different classic perspectives, namely product, process, press and
person. We discuss a set of ``easy'' and ``hard'' problems in machine
creativity, presenting them in relation to LLMs. Finally, we examine the
societal impact of these technologies with a particular focus on the creative
industries, analyzing the opportunities offered by them, the challenges arising
by them and the potential associated risks, from both legal and ethical points
of view.

Artificial Intelligence;Computation and Language;Computers and Society