$0$ s and $1$ s

Each term takes the number of $1$ s and the number of $0$ s in the previous term and concatenates them.

• Start with $1$
• $1$ has $1$ one and $0$ zeros, so $10$
• $10$ has $1$ one and $1$ zero, so $11$
• $11$ has $2$ ones and $0$ zeros, so $20$
• $20$ has $0$ ones and $1$ zero, so $01$
• $01$ has $1$ one and $1$ zero, so $\boxed{11}$

Since each term only depends on the previous one, the rest of the sequence will just be $20, 01, 11$ repeated indefinitely.