U.K. Brexit Secretary David Davis and EU Brexit negotiator Michel Barnier address media representatives in Brussels on August 31, 2017 | Emmanuel Dunand/AFP via Getty Images Brexit talks round 3 — what we learned The two sides remain deadlocked on major issues, but there was progress in the third round of talks on a number of fronts.

The third round of official Brexit talks left the two sides miles apart on the major issues. The U.K.'s Brexit Secretary David Davis described the talks as "high stress" but "productive," while his EU counterpart Michel Barnier observed, “we haven’t noted any decisive progress on the principal subjects.”

But despite some major roadblocks, both men noted several areas in which progress was made.

Neither side has issued any official documents setting out the precise nature of any agreement, but here is POLITICO's assessment of progress based on what both men had to say in the concluding press conference and briefings from EU officials and diplomats.

You can watch Barnier's closing remarks here and Davis' here.

1. CITIZENS' RIGHTS

Definition/scope of rights

Davis said both sides agreed on the reciprocity of certain rights for EU citizens in the U.K. (and vice versa), including on the right to establish a mutual recognition of professional qualifications. But an EU official with knowledge of the talks said there was no precision on the personal scope of rights and how they will be enforced. “So who are the people covered? What rights are covered?" they asked.

State of play: Some agreement but needs clarification.

Health care and social security

Both sides said commitments were made on the need to protect pensions, existing health care rights and how to cover the future social security costs of EU citizens living in the U.K and U.K nationals living in EU countries. "That's good news for example for British pensioners in the EU. It means that they will continue to have their health care arrangements protected," said Davis.

State of play: Shared commitments.

Cross-border workers

People who live in one member country and work in another are protected from discrimination under EU law. Both sides said an agreement was underway but didn’t go into specifics.

State of play: In progress, but mood music is good.

EU health insurance card

The EHIC card is free to EU citizens and gives access to medically necessary, state-provided healthcare in EU countries plus Iceland, Liechtenstein, Norway and Switzerland during a temporary stay. The EU agreed to extend the EHIC to British citizens living in the EU. But they refused to talk about extending it to EU citizens living in the U.K., saying that would be a future relationship issue. David Davis claimed it was “good news” for British pensioners.

State of play: No breakthrough.

Enforcement of rights

The EU and the U.K still have a fundamental disagreement on how the rights of EU citizens in the U.K. will be enforced. The EU says it should be done by the European Court of Justice, the U.K. says its own legal system is adequate. The EU, Barnier said, needs to “make sure that citizens' rights are directly enforceable in front of national jurisdictions, under the control of the ECJ, on which we disagree today.” He added that there had been clarification on pending legal cases involving the U.K.

State of play: Some clarification but sharp disagreement remains.

2. FINANCIAL SETTLEMENT

Another point of fundamental disagreement. On Tuesday, the U.K. presented a detailed legal analysis picking apart the EU's case for Britain's Brexit bill. "The Commission has set out a position and we have a duty to our taxpayers to interrogate it rigorously," said Davis, adding "It's fair to say ... we have a very different legal stance."

It didn't go down well.

Neither side "was in a capacity to find common grounds" in this area of negotiations, an EU official familiar with the talks said.

Davis reiterated that the U.K recognized they had "international obligations" and that some of their financial obligations would survive beyond their withdrawal. "We expected them to give more details on these obligations," an EU official said — something the U.K. has so far refused to do.

State of play: Deadlock

3. IRELAND/NORTHERN IRELAND

Common Travel Area

The CTA is a free-travel zone between the Republic of Ireland, the U.K., the Isle of Man and the Channel Islands which dates from the 1920s. In its position paper on Northern Ireland, the U.K. said it "wants to continue to protect the CTA and associated reciprocal bilateral arrangements." At the press conference, Barnier said there had been "genuine progress" on the issue as part of "fruitful" discussion on Northern Ireland. Davis agreed there was a "high degree of convergence."

State of play: Progress, but EU wants more detail from the U.K.

Good Friday Agreement

The Good Friday Agreement, signed in 1998, created the democratically elected Northern Ireland Assembly, plus cross-border institutions, and underpins the peace process. The EU saw a recognition on the U.K side that “this is more complex than perhaps initially imagined because a lot of north-south cooperation on the island is built on the EU legal framework," the EU official said. But the EU wants more detail from the U.K. on how exactly to preserve the benefits and the gains of the Good Friday Agreement in order to maintain peace. Barnier said negotiators were "able to clarify work that still needs to be done in a constructive spirit."

State of play: Good progress.

4. EURATOM

The U.K.'s exit from the EU's nuclear program Euratom was also discussed and Davis said the negotiators were "well placed to make even more progress in the next round" of talks in September.

State of play: To be continued.

5. TARIFF RATE QUOTAS

These are mechanisms under which the EU imports agreed tonnages of meat, sugar and grains from around the world with lower-than-usual duties. Neither Davis nor Barnier mentioned them in the closing press conference, but senior EU officials have told POLITICO that both sides are close to an agreement that they can present to the World Trade Organization.

State of play: Deal nearly done.

6. OTHER SETTLEMENT ISSUES

Davis said both sides reached "almost complete agreement" on the so-called "privileges and immunities" that the EU, its agencies and officials will enjoy on U.K. soil (and vice versa) post Brexit. He said the same applies to a "mutual approach" to confidentiality requirements on shared information.

State of play: Close to agreement.