Spy x Family is a 'normal' family; Dad and Mom and little daughter Anya.
The setting for the activity of this interesting trio is a region of the world (unspecified) in which two fairly good sized countries share a long and historic border, Westalis and Ostania. The two nations have apparently a rivalry that has lasted for some time with the competition breaking out in battle on occasion. The current state of affairs is one of a tenuous peace but there are many in the Westerian government who are very nervous of a major political figure in Ostania, Donovan Desmond who heads the National Unity Party. Monitoring his activities to be ready for any major shift in policy has become a prime objective.
Enter one of the very best agents in Westalis' intelligence community, a man known only as Twilight. In our introduction to him, we are told he "was a veteran of the battlefield, employing a hundred different faces to survive". Twilight is a master of disguise so he can appear as just about anyone if he put his mind to it. When not in makeup, he is a very handsome youngish-looking man with short blond hair, blue eyes, and pale white skin. While his exact age is not known, based on his looks and his superb athletic build, it is reasonable to place him in his late 20s (he claims early on that he has been an agent for "10-odd years"). His lack of real name is indicative of his nature to shed himself of anything of his past so he can devote himself to serving his country.
The instructions for Twilight to accomplish the mission of monitoring Desmond is to create an identity and get enroll that fake person's pretend child in an elite private school Desmond's son attends, thereby making opportunities to mingle with Desmond and his associates.
Twilight immediately comes up with, using Westalian Intelligence assets, the new identity of Loid Forger, psychiatrist, getting a nice apartment in the capital city of Berlint. For the requisite child Twilight visited several less-than-reputable orphanages in that city knowing that with the right amount of money, questions would not be asked and documentation would not be necessary. Wanting a child who could already read and write so as to fit in at the private school, Twilight decided on the young Anya.
This little girl is roughly five years of age. Short in stature with fair skin, light pink hair, and green eyes, Anya is very shy around strangers but immediately takes to Twilight and he, to a lesser degree, to her. What Twilight does not know and Anya is not at all willing to tell him is that she is only recently arrived at the orphanage having been born and partially raised in a secret facility run by a mysterious and unknown organization. Her big secret is that she is a telepath, which allows her to probe the minds of those close to her. This is how she was able to know that Twilight was a spy who needed her but had no bad plans for her. She also saw her opportunity to get out of a very unpleasant group home.
Filling out this 'family' to meet his bosses' instructions and the private school's requirement, Twilight made use of a list of all age-appropriate single women in Berlint. While out buying clothes for Anya, he encounters the beautiful but extremely shy Yor Briar. That woman is in an uncomfortable situation of having lied to her brother and only relative that she was seeing someone and was expected to produce pictures of him. When Twilight makes his bizarre pitch of her taking the role of his wife and mother to Anya, she sees a solution to her problem.
Yor is 27 years old. Her day job is that of an ordinary clerk at Berlint's city hall. She is a very attractive, fairly tall woman with fair skin, long black hair and "upturned red eyes". She comes across as a woman terribly lacking in social skills which makes her seem extremely shy to some people and coolly aloof to others. These traits are not fake; she really is shy and aloof and in many ways very naive and gullible. She does, however, have one impressive secret. She lives a secret life as highly trained and extremely deadly assassin known as the Thorn Princess working for a secret Ostanian organization. Her list of accomplishments (i.e., kills) is remarkable.
Thus we have the Forger family. Husband and father Loid who is really a famous foreign spy but his 'wife' has no inkling of that part of him. Wife and mother Yor who is really a highly skilled and fierce assassin but her 'husband' has no clue about that extracurricular occupation. And Daughter Anya whose telepathic abilities lets her know the truth about both her 'parents' but who knows a good thing when she sees it so not only does not snitch, she helps keep the covers intact.
And while this deception goes on and the monitoring of Desmond takes place, many side missions for both Twilight and the Thorn Princess keep their lives exciting and interesting.