This is CNBC's live blog covering European markets.

European markets closed higher on Tuesday as investors in the region digested inflation data and corporate earnings releases.

The pan-European Stoxx 600 index ended the session up 0.32%, with mining, utilities and construction stocks among the few sectors in negative territory.

Major bourses were in mixed territory, with the FTSE 100 down by around 0.05%.

Annual inflation in the euro zone rose to 2.4% in December, a flash estimate from Eurostat showed on Tuesday, up from 2.2% in November. The print — which was in line with expectations, according to a Reuters poll of economists — was lifted by high services costs and rising energy prices.

Preliminary data from French statistics agency Insee on Tuesday, meanwhile, showed prices in France rose less than expected in December. The country's euro zone-harmonized consumer price index was up 1.8% year-on-year, less than the 1.9% anticipated by economists polled by Reuters.

The French figures come a day after German inflation data showed the country's consumer price index jumped to a higher-than-expected 2.8% in December. Analysts polled by Reuters expected a 2.6% reading.

In auto news, shares of Volvo Cars closed up around 9.25% after the Swedish carmaker reported a new global sales record for 2024.

Overnight, Asia-Pacific markets rose Tuesday, following Monday's rally in technology shares on Wall Street that saw the S&P500 and Nasdaq Composite post back-to-back gains.

U.S. stocks opened higher on Tuesday morning, with the Dow, S&P 500 and Nasdaq Composite all slipping into the red later in the session.

Correction: This blog has been updated to reflect that German statistics agency Destatis corrected its year-on-year harmonized inflation figure to 2.8% in December.

European markets close higher

European markets closed higher on Tuesday as investors digested fresh inflation data and corporate earnings releases.

The pan-European Stoxx 600 index ended the session up 0.29%, with the majority of sectors and major bourses in the green.

Germany's DAX closed up 0.66%, France's CAC gained 0.72% and Italy's FTSE MIB also rose 0.49%. The U.K.'s FTSE 100 index, meanwhile, dipped 0.09%

— Karen Gilchrist

U.S. stocks open higher

U.S. stocks opened higher on Tuesday, with the S&P 500 rising for the third day.

The S&P 500 was up 0.23% in early deals, while the Dow Jones Industrial Average was up 0.45%. The Nasdaq, meanwhile, dipped around 0.06%.

— Karen Gilchrist

Kion shares surge 10%

Shares of German industrial trucks manufacturer Kion Group jumped more than 9.5% on Tuesday, lifting the company's stock to the top of the Stoxx 600.

It came after the company announced it had teamed up with Accenture and tech giant Nvidia to bring AI-powered robots into its supply chains.

—  Chloe Taylor

UK borrowing costs rise

U.K. borrowing costs ticked higher on Tuesday, following an auction of 30-year Treasury gilts that saw yields on the long-term bonds hit their highest level in almost three decades.

By 12:04 p.m. London time, the yield on the 30-year gilt — a U.K. government bond — climbed 3 basis points to 5.214% — its highest level since the late 1990s.

The move came after the U.K. Debt Management Office auctioned off £2.25 billion ($2.83 billion) worth of gilts with a 30-year maturity, with an initial yield offer of 4.375%.

Yields on gilts with shorter maturity terms also moved higher on Tuesday.

The U.K.'s 10-year gilt yields gained 3 basis points to trade at 4.650%, while yields on 2- and 5-year gilts added around 2 basis points, respectively, by the early afternoon.

— Chloe Taylor

U.K. retail sales grew 0.7% in 2024

U.K. retail sales grew 3.2% year-on-year in the four weeks to Dec. 28, the British Retail Consortium said on Tuesday, lifted by Black Friday sales. Food sales growth in the run-up to the holiday season slowed, with the category recording annual growth of 1.7%, compared to the 6.3% seen in the year to December 2023.

For the whole of 2024, retail sales grew at an annual rate of 0.7%, according to the BRC figures, while the final quarter of the year — the so-called "Golden Quarter" — logged annual sales growth of 0.4%.

The final three months of the year "failed to give 2024 the send-off retailers were hoping for," BRC CEO Helen Dickinson said, attributing the figures to weak consumer confidence and to a challenging economic backdrop.

— Chloe Taylor

Volvo reports record sales

Shares of Volvo were up more than 4% by 9 a.m. London time, after the Swedish carmaker reported a new global sales record for 2024.

In an update on Tuesday, Volvo said it sold 763,389 cars during the year, an increase of 8% from 2023. The figures were lifted by demand for its electrified models, with Volvo's fully electric cars seeing annual sales growth of 54% in 2024 to account for 46% of the company's car sales last year.

— Chloe Taylor

French inflation rises less than expected to 1.8% in December

French prices rose less than expected in December, preliminary data showed on Tuesday in the country's first inflation print since Francois Bayrou was appointed prime minister.

The euro zone-harmonized Consumer Price Index was up 1.8% in the year to December, national statistics agency Insee's provisional results showed. Economists polled by Reuters had anticipated a 1.9% rise from a year earlier.

On a monthly basis, prices were shown to have risen by 0.2%, following a monthly contraction of 0.1% in November.

— Chloe Taylor

UK house prices rose 3.3% in 2024, Halifax says

The average house price in the U.K. were up 3.3% in the year to December, British lender Halifax said on Tuesday, with a typical home costing £297,166 ($372,959) by the end of 2024.

However, Halifax noted in its December House Price Index that prices had fallen 0.2% between November and December, following five consecutive monthly price rises.

— Chloe Taylor

Sodexo’s first-quarter revenues rise

French food services firm Sodexo reported a 4.6% year-on-year jump in first-quarter organic revenue growth on Tuesday, and kept its full-year fiscal guidance unchanged.

The company's consolidated revenues for its fiscal first quarter came in at 6.4 billion euros ($6.7 billion). It said it expected organic revenue growth for fiscal 2025 to be between 5.5% and 6.5%, with modest growth in the first half of the year followed by an acceleration in the following six months.

— Chloe Taylor

CNBC Pro: Here are Europe's top ETFs that outperformed in 2024 — including some that gained 30%

U.S. stocks ended 2024 on a high, with the S&P 500 finishing last year with gains of over 23%.

While funds tracking the major indices will have logged similar returns, a handful of actively managed ETFs marketed in Europe outperformed, including JPMorgan's US Research Enhanced Index Equity ETF and Invesco's Quantitative Strategies ESG Global Equity Multi-Factor ETF. 

CNBC Pro screened 321 ETFs in Europe that are invested in equities, fixed income, or commodities, and are not leveraged or produced inverse returns.

Two of the ETFs returned 30% last year.

CNBC Pro subscribers can read more here.

— Ganesh Rao

Oil and gas exploration stocks head for 10th straight advance in longest rally in almost five years

The SPDR S&P Oil & Gas Exploration & Production ETF traded higher on Monday, rising as much as 2% intraday, putting the ETF on pace for its 10th straight gain for the first time since April 2020.

The 55-stock XOP is up nearly 10% over the past 10 sessions, its best 10-day period since mid-October 2023. It was recently just up about 0.1%.

The longest rally ever for XOP was an 11-day advance that ended in November 2010. The exchange traded fund now has roughly $2 billion in assets, according to FactSet data. Its five largest positions are Antero Resources, APA Corp., Diamondback Energy, Occidental Petroleum and Coterra Energy.

Although XOP remains below its April 2024 52-week high, the ETF is moving above its 50-day moving average for the first time since early December.

— Scott Schnipper, Nick Wells

Trump reportedly eyes narrower tariff plans, auto stocks jump

President-elect Donald Trump is reportedly planning to narrow his tariff plans to target only certain important sectors, instead of all imports, the Washington Post reported, citing people familiar with the matter.

Two weeks before he takes White House, Trump is discussing plans to pare back some of the sweeping, universal tariffs he vowed to implement on the campaign trail, the Post reported. Instead, he is aiming to impose duties on sectors that are viewed critical to national or economic security, the newspaper reported, adding that the discussions are not final.

Shares of automakers jumped in premarket in a relief rally. Ford and General Motors climbed more than 2% each, while Stellantis NV surged 7% in early trading.

— Yun Li

European markets: Here are the opening calls

European markets are expected to open lower Tuesday.

The U.K.'s FTSE 100 index is expected to open 40 points lower at 8,200, Germany's DAX down 87 points at 20,123, France's CAC down 33 points at 7,414 and Italy's FTSE MIB down 172 points at 34,696, according to data from IG.

Traders will be keeping an eye on preliminary inflation data in the euro zone in December, as well as the bloc's unemployment rate in November.

— Holly Ellyatt