Crito
The dialogue takes place in Socrates' prison cell, where he awaits execution. He is visited before dawn by his old friend Crito, who has made arrangements to smuggle Socrates out of prison to the safety of exile. Socrates seems quite willing to await his imminent execution, and so Crito presents as many arguments as he can in order to persuade Socrates to escape. On a practical level, Socrates' death will reflect badly on his friends--people will think they did nothing to try to save him. Also, Socrates should not worry about the risk or the financial cost to his friends; these they are willing to pay, and they have also arranged to find Socrates a pleasant life in exile. On a more ethical level, Crito presents two more pressing arguments: first, if he stayed, he would be aiding his enemies in wronging him unjustly, and would thus be acting unjustly himself; and second, that he would be abandoning his sons and leaving them without a father.
Euthyphro
Euthyphro has come to present charges of murder against his own father who, after arresting one of his workers for killing a slave from the family estate on Naxos Island, tied him and threw him in a ditch where he died of exposure to the elements without proper care and attention (3e–4d) while Euthyphro's father awaited to hear from the exegetes ("cf." Laws 759d) about how to proceed. Socrates is astonished by Euthyphro's confidence in being able to prosecute his own father for the serious charge of manslaughter, despite the fact that Athenian Law allows only relatives of the dead man to file suit for murder. (Dem. 43 §57) Euthyphro dismisses the astonishment of Socrates, which confirms his overconfidence in his own critical judgment of matters religious and ethical.