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Francesco Totti, two days short of his 40th birthday, scored his 250th Serie A goal for AS Roma on Sunday but it was not enough as they lost 3-1 at Torino.
In the week of his 31st birthday, Messi was again a largely anonymous figure as they lost 4-3 to France in a thrilling last-16 match in Kazan.
Carlos Tevez has been included in the squad for the first time in three years for next month's friendlies in England against Croatia and Portugal.
Argentina's experimental line-up proved too strong for an outclassed Singapore in their international friendly on Tuesday, with the South Americans swatting aside their hosts 6-0 and the opening five goals coming from first-time scorers.
Cristiano Ronaldo was involved in all three of his team's goals as Juventus came from behind to beat Napoli 3-1 in a Serie A top-of-the-table clash on Saturday to maintain their perfect start to the season.
Europa League favourites Manchester United secured a 1-1 draw on a threadbare pitch at Rostov, while Olympique Lyonnais beat AS Roma 4-2 helped by a fine individual goal from Nabil Fekir in their last 16, first leg ties on Thursday.
Barcelona capitalised on two disastrous own goals by A S Roma to thrash the Italian side 4-1 at the Nou Camp on Wednesday and take a huge step towards reaching the Champions League semi-finals for the first time in three years.
Diego Costa scored twice as Atletico Madrid beat Valencia 3-0 to maintain their winning home run this season and keep pace with Barcelona at the top of the La Liga table.
The Portuguese forward then fired in the penalty in the sixth minute of stoppage time.
Inter Milan's aversion to Europa League football continued with a 3-1 defeat at Sparta Prague, while AS Roma ended a continental hoodoo stretching back seven games with a 4-0 home win over Romanian side FC Astra on Thursday.
Photos from the La Liga matches played on Sunday
News of all that's transpired on and off the football field
Manchester City squandered a gilt-edged opportunity to close the gap on Premier League leaders Chelsea when they let slip a two-goal lead to draw 2-2 at home to struggling Burnley on Sunday.
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IMAGES from the Champions League matches played on Tuesday
Manchester United goalkeeper David de Gea added another heart-stopping save to his collection as his team held a highly-impressive Sevilla side to a 0-0 draw away from home in the first leg of their Champions League last-16 tie on Wednesday.
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Lionel Messi's penalty earned Argentina a 2-1 win over Croatia after a fortunate equaliser that stood despite an unintentional handball by Sergio Aguero in a friendly at West Ham United's Upton Park ground on Wednesday.
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The victory saw the unfashionable Madrid club tighten their grip on the coveted fourth spot in the table by moving on to 58 points after 36 games, three points clear of nearest challengers Sevilla, who lost to Leganes on Friday.
News of all that's transpired on and off the football field
