Currently there are 4 main Shipping alliances. The Crurrent Alliances are G6, Ocean Three, 2m, and CKYHE. these will all be changing in early 2017 due to mergers and acquisitions. Currently CKYHE does not call in Halifax.
The G6 Alliance consists of American President Lines (APL), Hapag-Lloyd, Neptune Orient Line (NOL), Hyundai Merchant Marine, Mitsu OSK (MOL), Nippon Yusen Kaisha (NYK) Line and Orient Overseas Container line(OOCL). the
Ocean Three Alliance consists of CMA-CGM,China Shipping Co. Ltd. (CSCL) and United Arab Shipping Co.(UASC).
the 2m Alliance, is not surprisingly made up of Maersk line and Mediterranean Shipping Co.(MSC). only Maersk makes a weekly call in Halifax. the CKYHE Alliance consists of Cosco Container Lines, “K” Line, Yang Ming Line, Hanjin Shipping, and Evergreen Line.

these alliances are getting a big shakeup. Hyundai Merchant Marine is Joining the 2m Alliance for 2017.

In the past year, CMA-CGM (Ocean Three) Bought APL (G6) and NOL (G6) and COSCO (CKYHE) and CSCL (Oceans Three) were merged into  China Cosco Shipping by the Chinese government. They will be joined by OOCL and Evergreen line to form the Oceans Alliance (Route Details)

Also HAPAG-Lloyd (G6) merged with CSAV in 2014 and bought UASC (Oceans Three) in 2016. it was also announced this year that NYK (G6), MOL(G6) and K Line (CKYHE) are merging into a new entity. Hanjin recently went Bankrupt.
these lines, along with Yang Ming have formed The Alliance (Route List), although Hanjin will likely be sold or Liquidated.

ZIM restructuring due to high debt, but so far is remaining independent. ACL is also remaining independent, though it currently has slot Charters with Hapag-Llyod, and predicts growth with their new G4 Series ships. Bahri, Nirint, Melfi, Eimskip, Oceanex all run smaller specialized services, focused on supplying small geographic areas and are likely unaffected by the shakeups of the larger lines.

UPDATE: After this post was initially posted, tropic shipping announced they will be moving to Halifax from Saint Johns NB in January 2017. This will add a weekly call to the Caribbean.