The first season of His Dark Materials was a reasonably solid adaptation of Philip Pullman's novel Northern Lights (retitled The Golden Compass in the US). It took advantage of its eight-hour running time to deliver a more in-depth, thoughtful and resonant version of the story than the perfunctory 2007 movie, although it may have also had a little bit too much time, with some issues with pacing. The season also suffered from a surprisingly subdued performance by Dafne Keen as the spirited Lyra (a problem of direction, not the actress, it should be emphasised) and a distinct lack of daemons in scenes which should have had lots of them in evidence.
Season 2 is an improvement on every single level. With seven episodes to adapt the second book in the trilogy, The Subtle Knife, the pacing is punchier and works better. Keen is more energetic and more in keeping with the Lyra from the books, and the show is positively awash with daemons when necessary. HBO came on board the project whilst the first season was filming, so it looks like their cash injection helped the second season overcome some of the budgetary constraints that were a little more evident in the first season (despite reports of this being one of the most expensive BBC dramas ever made).
Some complaints may be unavoidable ones from the book: the abrupt jettisoning of much of Season 1's supporting cast feels a little jarring (especially the near-total absence of Asriel), and Pullman's intellectual approach and thematic ideas sometimes makes this a story more told from the head than the heart. But the escalating tension and increasing ruthless streak (especially from Ms. Coulter) also make the season more tense and unpredictable, at least to those who have not read the books.
The second season of His Dark Materials (****½) improves over the prior outing on almost level, being more epic, better-written and more impressive in scale and scope. It is available to watch via the BBC iPlayer in the UK and HBO in the United States.
A third season, depicting the final book in the trilogy, The Amber Spyglass, is in the planning stages but has not yet been greenlit.