Ferroelectric thin films have been intensively studied and used for a variety of electronic devices thanks to their spontaneous and switchable polarization (P). My study of P switching dynamics in ferroelectric capacitors with a modified piezoresponse force microscopy revealed that the nucleation of reversed domains occurs at particular points, i.e. random-field disorders, with a broad distribution of nucleation barrier energy. In a thinner ferroelectric capacitor, a stronger depolarizing field (Ed) totally changes P behaviors by lowers a stability of P. I measured Ed experimentally for the first time and found that the measured Ed values agree well with simple electrostatic calculations, indicating that this inevitable Ed sets a harder thickness limit for ferroelectric applications. Later, while strain engineering enables only a few unit-cells of ferroelectric layer by enhancing P stability, quantum tunneling makes ferroelectric capacitors useless. However, it is found that the tunneling current through a ferroelectric ultrathin layer depends on its polarization direction as a resistive switching. Furthermore, I found stable multi-level resistance states of ferroelectric tunnel junctions which can be tuned continuously by different amplitude and duration of external electric field, being useful for high-density memory devices and brain-mimicking learning networks. My subsequent finding that a significant resistive switching in a ferroelectric hexagonal rare-earth manganite thin film suggests that the hexagonal ferroelectric thin films are unprecedented candidates for ferroelectric memristors with possible photo-induced effects.