Penelope tested Odysseus three times in the "Odyssey." With Odysseus disguised as a beggar, she asked him about Odysseus' travels, clothing and personality. In her second test, Penelope retrieved Odysseus' bow, stating she will marry the man who strings it and makes a perfect shot. For her final test, she requested the movement of their marriage bed, which only Odysseus knows cannot be moved.
When Odysseus returned to Ithaca, he kept his identity hidden, acting as a beggar. His son, Telemachus, brought Odysseus to his home and treated him to a meal. Odysseus has a chance to converse with Penelope, but neither revealed their true intent or feelings, remaining critical and thoughtful instead. She asked the beggar, who claimed to have come across the hero, about the fate of Odysseus. It is implied that Penelope, being Odysseus' equal in mind, suspected the beggar's true identity.
Penelope's second test was meant to undoubtedly prove to all parties that Odysseus had returned. Choosing a competition of arms gave Odysseus a strong advantage over the inexperienced suitors. Penelope likely considered this prior to assigning the test. She also acted slightly flirtatious with the suitors for the first time, to make them believe they had a chance and to spur the still-disguised Odysseus to string his bow and retake his home.
The test of the marriage bed was her final one. Penelope had conveniently been asleep in her bedroom during the competition and subsequent slaughter of the suitors. Scholars generally agree that she was most definitely certain, at this point, that the man was Odysseus, but she continued to test him one last time. She orders her maids to remove her marriage bed from its current room. The room had been closed off since Odysseus went to war. He responded in outrage at the thought, as one of their bedposts was a still-living tree.