There are two distinct views of what happened to Madeleine McCann.
The primary Portuguese police investigator, Goncalo Amaral wrote a book, THE TRUTH OF THE LIE, and is of the opinion that the parents, Kate and Gerry McCann accidentally killed their daughter, Madeleine with a sedative and then covered up the crime.
Kate McCann wrote a book, MADELEINE defending she and her husband from all the accusations that has them involved in the disappearance of their child.
Robert Murat, an Englishman, living with his mother, next door to the McCann's holiday apartment became a suspect very early on, but no solid evidence could ever be discovered that would link him to the disappearance.
There is a lot of discussion about the window in the room that Madeleine was sleeping. Kate claims that is was open when she arrived. No one else remembers seeing it open after the disappearance. This small detail along with a lot of other discrepancies caused the Portuguese police to question the involvment of the parents.
Because of the politics of this case, the Portuguese police were hampered in their attempts to thoroughly investigate this case.
For instance, they tried to reconstruct the night of the disappearance, but never got the cooperation of the McCanns or the other friends who were traveling with them.
The press complicated everything and were primarily on the side of the McCanns.
An Irish family who were returning to their holiday apartment reported that they saw a man carrying a child around 9:55 on the night of the disappearance. They didn't think anything about it until they returned to Ireland and saw a report on the disappearance and realized they might have seen the abductor. Later when Gerry and Kate returned to England, the Smiths saw Gerry getting off the plane and said that it who they saw carrying the child.
One of the most important events that came out of the investigation was the use of Martin Grime's cadaver and blood dogs to search the McCann's apartment and the clothes and cars of anyone involved. The dogs found traces of blood and cadaver in two (2) locations in the apartment and 2 locations of the McCann's rented car.
Then the DNA results created another controversy with the Portuguese police saying the results are conclusive enough and the McCanns' saying that they're not conclusive and flawed.