On 1 March about 27,000 Iraqi troops commenced their attack on Tikrit, a city 150km (93 miles) north of Baghdad that has been occupied by Islamic State (IS) since June 2014.
The assault is the first attempt to evict IS from a major urban centre that they have controlled and fortified, a test case for the planned operation to retake Mosul - the Iraqi capital of the IS caliphate.
The Tikrit operation will be scrutinised to shed light on two main uncertainties.
Can predominately Shia volunteer forces play a productive leading role in operations within Sunni communities? And can the Iraqi military dislodge IS defenders from fortified urban settings?
The assault has been billed as a joint operation involving the Iraqi army, the paramilitary federal police, the Iraqi Special Operations Forces (ISOF), and the predominately Shia Popular Mobilisation Units (PMU), the volunteer brigades and militias that have been formally integrated into the security forces since June 2014.
The one element conspicuously absent from the mix is the US-led international coalition.
No requests for coalition air strikes have been made by the Iraqi government, a common feature of operations led by the PMUs. Indeed, some 18,000 PMU fighters are providing the bulk of the troops for the assault.
The PMU are led by Abu Mahdi al-Muhandis, who was labelled by the US as a "specially designated global terrorist" in 2009 for his part in attacks on US forces and other targets.
He and many other PMU commanders have worked intensively with Iran's Revolutionary Guard, and continue to draw Iranian and Lebanese Hezbollah advisers into their operations.
The apparent exclusion of coalition support by Iranian proxies was confirmed by Gen Martin Dempsey, chairman of the US Joint Chiefs of Staff, who stated on 3 March that the battle had seen "overt conduct of Iranian support, in the form of artillery and other things".
Though Tikrit itself has been largely depopulated, the behaviour of the predominately Shia PMU forces - who are not subject to Iraqi military discipline - will be closely watched as they clear IS fighters from rural Sunni communities.
If the attack on Tikrit is successful it may increase the likelihood that Iraq will replicate the model further north in Mosul, deploying PMU units to bolster the Iraqi military effort to retake the city of one million, the capital of Sunni Iraq.
This might again preclude or complicate international support for the operation.
Though the battle of Tikrit will provide many insights into the offensive urban warfare capabilities of Iraqi government forces, it is a stretch to say that the Tikrit operation is an accurate predictor of the outcome of a battle for Mosul.
Tikrit is relatively close to Baghdad, and Iraq forces have been operating in Tikrit's vicinity since August 2014.
In contrast, Mosul is 350km north of Baghdad, and about 150km north of the most advanced Iraqi army outposts at Beyji. Just projecting Iraqi forces up to Mosul and supplying them will be a major logistical challenge.
Tikrit is also small - the city itself is only 15sq km versus the 400sq km sprawl of Mosul city.
Ammar Hikmat, the deputy governor of Salahuddin province, where Tikrit is the provincial capital, told the Associated Press that soldiers had found about 100 mines and bombs on a single 8km stretch of road.
IS is likely to contaminate many areas within Mosul in this fashion, creating a mass of explosive hazards and buildings to be painstakingly cleared.
And urban Tikrit is almost wholly depopulated whilst IS has deliberately kept over 750,000 citizens in Mosul.
There is no guarantee that Mosul's independent-minded citizenry, which is well over 65% Sunni Arab, will welcome PMU forces. The PMUs could also get bogged down in indecisive operations in Tikrit and other areas short of Mosul.
These outcomes could throw the weight of the operation on the US-supported Iraqi army, which is marginally better respected by Mosul's citizens.
The operational concept outlined by a US official in a much-discussed 19 February briefing suggested that eight Iraqi army brigades would take the lead in liberating Mosul.
Preparing Iraqi army units for the Mosul battle is potentially the slowest aspect of the effort to liberate the city and could stretch into the summer, derailing a possible start date for the operation in April or May.
The Iraqi army remains in very poor shape, boasting a frontline combat strength of about 48,000 troops versus nearly 210,000 at the height of its effectiveness in 2009.
The Mosul fight is scheduled to draw at least three of the army's stronger remaining brigades north from Baghdad, halving Iraqi military strength in the capital.
This will leave Iraq's government centre largely secured by the Shia PMUs and ministry of interior units, which are also led by Iranian-backed fighters with connections to Iran's Revolutionary Guard that span decades.
One of the unintended consequences of the fight to retake Mosul could be a critical weakening of state control of the security portfolio in Baghdad itself, a situation that may prove difficult to remedy in future years - as history has shown in other regional capitals such as Beirut and Tripoli, Libya.
Dr Michael Knights is the Lafer Fellow at the Washington Institute for Near East Policy. He has worked in all of Iraq's provinces, including periods spent embedded with the Iraqi security forces. His recent report on the Iraqi security forces is available via the Washington Institute website.