"Things that cause people to stumble are bound to come ..." (Luke 17:1-2)

"Things that cause people to stumble are bound to come, but woe to anyone through whom they come. It would be better for them to be thrown into the sea with a millstone tied around their neck than to cause one of these little ones to stumble." (Luke 17:1-2)

Who are the 'little ones'?

Jesus is speaking to his newest followers here. Furthermore, the phrase "little ones" is being translated from the Greek word μικρός (mikros).

This means, according to the lexicon:
"small, little -
1) of size: hence of stature, of length
2) of space
3) of age: less by birth, younger
4) of time: short, brief, a little while, how little!
5) of quantity: i.e. number, amount
6) of rank or influence"

So is Jesus speaking of "little ones" as those who are physically shorter? Or lived in small spaces? Or were younger? Or perhaps only a few people? We also find among these meanings, "small, little - of rank or influence."

Jesus is referring to those who are new followers - who are growing in their spiritual progress. They are new followers. He is referring to new students - those who have just come to learn from Jesus. And yes, it may also include some younger people as well - who are hearing Jesus for the first time or two.

Jesus speaks this to his students because he wants his students to be positive influences for those who are just coming to hear Jesus' teachings, and considering following Jesus. And he doesn't want any of his students to interfere in their spiritual progress.

Because they are new students, their spiritual progress is a little tender. It is like a small plant sprout. It needs to be cared for and protected as it grows.

What does he mean by 'stumble'?

By "stumbling" (from the Greek word σκανδαλίζω (skandalizō) - which means "to cause one to trip or fall" or to "entice to sin") Jesus is speaking of the potential of some of his students influencing the newer students negatively - somehow causing them to fall away from Jesus' teachings and go back to their old ways. Or otherwise, be influenced into materialistic activities.

Such a thing can occur from a number of activities outside of simply being a bad example. This includes fanaticism. A fanatical follower - someone intent on proving to others that he or she is a great follower - can easily blow a new student away. And an insincere groupie follower - one whose focus is to join a group in order to fit in and be liked but isn't sincerely interested in sincerely taking the teachings within and following the teachings - can easily scare off a new student.

The Gospels indicate that Jesus had many followers - each at different levels of relative advancement. As such, he had to instruct and accommodate both those who had been following him for a while as well as new followers. Here we find Jesus is instructing those who had been his followers/disciples to be alert to their actions and their influence upon new students - those who were hearing from Jesus for the first time and trying to learn his teachings regarding loving service to the Supreme Being.

What does Jesus mean by this? Who are the "little ones" and what does he mean by causing them to stumble?

Who is Jesus saying this to?

Jesus is speaking directly to his disciples and students:
Jesus said to his disciples: (Luke 17:1)
The Greek word translated to "disciples" here is μαθητής (mathētēs). According to Thayer's lexicon and other references, this word can mean "learner," "pupil" and "disciple" - and more literally, "one who follows one's teachings."

Thus we find a misnomer among many institutional translations of the New Testament. We find an attempt to detail that Jesus only had 12 disciples, and these were the only people who could represent him in their own preaching affairs.

This erroneous interpretation was furthered by the Roman Catholic institution, which proclaimed that since Jesus supposedly only had 12 disciples - and they were all male, therefore only men can be priests - or bishops, popes, and so on. Such an interpretation does not embrace what Jesus taught at all.

Did Jesus have more than 12 disciples?

Yes, Jesus had many students and disciples - many of whom were women. We find at least three of his closest students and likely also disciples were women - and quite certainly many others. Multiple women followers of Jesus were named Mary, we find Mary Magdalene; Mary of Jacob, who was the mother of James the Less; Mary of Clopas; and Mary of Bethany. They each interacted with Jesus, and at least three of these followed Jesus.

We also find that Mary's sister Martha was a follower of Jesus. This may or may not be the same Mary as Mary Magdalene - because the scriptures introduce this Mary quite differently:
As Jesus and his disciples were on their way, he came to a village where a woman named Martha opened her home to him. She had a sister called Mary, who sat at the Lord's feet listening to what he said. (Luke 10:38-39)
Thus we see that this Mary certainly qualified to be one of Jesus' followers. Thus we find there are multiple women who ardently followed Jesus and his teachings. Some of these women were determined followers of Jesus. For example, when most of Jesus' male disciples had scattered, three stayed nearby Jesus during his crucifixion:
Near the cross of Jesus stood his mother, his mother’s sister, Mary the wife of Clopas, and Mary Magdalene. (John 19:25)
While the "twelve" disciples of Jesus had scattered for fear of being arrested, the three Marys - his mother, his aunt and Mary Magdalene - stood by Jesus' side during his persecution.

Then we find that it was Mary Magdalene and his mother who were checking up on Jesus' tomb.

And it was Mary Magdalene who was sent to tell the other disciples that Jesus had made a re-appearance.

So are we to say that these women were not Jesus' followers or even disciples? Certainly at least three of these women qualified themselves as sincere students and followers, achieving the role of μαθητής (mathētēs) - "one who follows one's teachings."

Indeed, Jesus had many disciples - at least 72 according to Luke 10:
After this the Lord appointed seventy-two others and sent them two by two ahead of him to every town and place where he was about to go. He told them, "The harvest is plentiful, but the workers are few. Ask the Lord of the harvest, therefore, to send out workers into his harvest field. Go! I am sending you out like lambs among wolves. Do not take a purse or bag or sandals; and do not greet anyone on the road. "When you enter a house, first say, 'Peace to this house.' If someone who promotes peace is there, your peace will rest on them; if not, it will return to you. Stay there, eating and drinking whatever they give you, for the worker deserves his wages. Do not move around from house to house. "When you enter a town and are welcomed, eat what is offered to you. Heal the sick who are there and tell them, 'The kingdom of God has come near to you.' But when you enter a town and are not welcomed, go into its streets and say, 'Even the dust of your town we wipe from our feet as a warning to you. Yet be sure of this: The kingdom of God has come near.' I tell you, it will be more bearable on that day for Sodom than for that town. "Woe to you, Chorazin! Woe to you, Bethsaida! For if the miracles that were performed in you had been performed in Tyre and Sidon, they would have repented long ago, sitting in sackcloth and ashes. But it will be more bearable for Tyre and Sidon at the judgment than for you. And you, Capernaum, will you be lifted to the heavens? No, you will go down to Hades. "Whoever listens to you listens to me; whoever rejects you rejects me; but whoever rejects me rejects him who sent me." The seventy-two returned with joy and said, "Lord, even the demons submit to us in your name." (Luke 10:1-17)

Did Jesus' disciples also baptize?

Furthermore, we find that Jesus had so many students and disciples that Jesus' disciples were also baptizing Jesus' followers. Here is what one of John's disciples told John about Jesus:
They came to John and said to him, “Rabbi, that man who was with you on the other side of the Jordan—the one you testified about—look, he is baptizing, and everyone is going to him.” (John 3:26)
So we find that not only did Jesus have at least 72 disciples, but he sent out 72 disciples to teach others what he had been teaching them - as well as perform healings and cast out demons. And some of his disciples were also baptizing others. So how can the Roman Catholic Church claim that Jesus only had 12 disciples and since they are men, priests can only be men?

The reality is that Jesus was not identifying with the physical body. This he clarified:
While Jesus was still talking to the crowd, his mother and brothers stood outside, wanting to speak to him. Someone told him, "Your mother and brothers are standing outside, wanting to speak to you." He replied to him, “Who is my mother, and who are my brothers?” Pointing to his disciples, he said, “Here are my mother and my brothers. For whoever does the will of my Father in heaven is my brother and sister and mother.” (Matt. 12:46-50)
This statement says a lot. It says that Jesus didn't identify with his physical body and the physical body of his family. His identity was linked with loving and serving God.

His statement also indicates that he did accept that women could serve him and be his disciples since he included "sisters" with his statement - indicating that there were women among his disciples and students.

The physical body - whether it be white, black, male or female - is only a temporary vehicle that we wear for a few years. Then we leave it behind at the time of death. This fact was confirmed by Jesus:
"Do not be afraid of those who kill the body but cannot kill the soul." (Matt. 10:28)
Why did Jesus teach this? The only conclusion is that we are not the physical body. We are the soul, the personality temporarily inhabiting the body. This is why Jesus said we don't have to fear those who kill the body.