To understand "Madame X" you need to realize it was based on a 1908 French play by Alexandre Bisson (1848-1912) that reflected 19th Century morality. It was filmed in 1916, 1929 (Ruth Chatterton directed by Lionel Barrymore), 1937 (this version), 1954, 1966 (Lana Turner), and 1981. The 1937 version reflects a slightly different morality, not only more recent, but also examined from an American POV rather than the European. Watching it in the 21st century, one has to take all these influences into account.
Gladys George (1904-54) plays Madame X and gives an excellent performance, her career best, and probably among the top 50 performances ever given on film. It's uncanny how she ages 20 years not only in appearance, but in manner, voice, etc. To modern audiences it may look a little over the top, but for the 1930s and set in the early 1900s, it isn't.
George was nominated for an Oscar for "Valiant is the Word for Carrie" (1936) but is probably better known as Jimmy Cagney's moll from "The Roaring Twenties" (1939) or Humphrey Bogart's dead partner's wife from "The Maltese Falcon" (1941).
Warren William (1894-1948) plays George's husband, a wealthy lawyer too proud to forgive Madame X her trespass, sending her away and setting in motion the sad story. William is best known for his role as d"Artagnan in "The Man in the Iron Mask" (1939) and as the first Perry Mason in a series of mid 30s films. His work here is quite good.
John Beal (1909-97) plays George's son, who thinks his mother is dead. Beal made nearly 100 films between 1933 and 1993, usually as a second male lead in B films. He's best known for his role as Judge Vail in TV's "Dark Shadow" (1970-71). He is effective in this role, meant for Tyrone Power, and his final scene with George is a real tear jerker.
Reginald Owen (1887-1972) as a friend of the family and Henry Daniell as a sleaze-bag blackmailer both do their usual good jobs in supporting roles.
Sam Wood directs. He hit his stride in the 30s with this film and "A Night at the Opera" (1935), "A Day at the Races" (1937), and "Goodbye Mr. Chips" (1939). He's also known for "Kings Row" (1942), "Pride of the Yankees" (1942) and "For Whom the Bell Tolls" (1943).
In addition to George's bravura performance, the film has some good looking transition effects and shows the passage of time in a creative way, at least by 1930s standards. The sex and violence are merely hinted at, yet nonetheless effective.
Bottom line - a memorable tear jerker with a truly great performance.