The violence comes as Iraqi forces prepare for an operation to retake Mosul, the last IS-held city in the country -- a key battle, but one that will not end the threat of attacks such as those carried out on Saturday.
In the deadliest attack, a suicide bomber targeted a funeral tent where mourners were gathered to pay their respects in the Shiite-majority Shaab area of north Baghdad, killing at least 34 people and wounding least 36, officials said.
A witness said the bomber entered the funeral tent and blew himself up as lunch was being served.
"I saw with my eyes 20 martyrs on the ground," the witness said.
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Blood stained the ground at the scene of the attack, which was littered with the remains of plastics chairs mourners had been seated on.
IS, a Sunni extremist group, considers Shiites to be heretics, and frequently carries out suicide bombings and other attacks against them in Baghdad and elsewhere in the country.
That attack led to a shakeup of senior Baghdad security officials and the announcement of other measures aimed at improving security in the capital, but the bombings have continued.
Also today, militants attacked two areas north of Baghdad, killing a further 12 people, according to police.
In Malha, an area east of the city of Tikrit, suicide bombers attacked a federal police position, killing eight and wounding 11, officers said.
There was no immediate claim of responsibility for those two attacks, but the Baghdad bombing was just the latest in a series that IS has said it carried out against Shiites in the capital.