diff --git a/Dockerfile b/Dockerfile
index e9361d4..0941ed3 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -93,7 +93,7 @@ RUN cd /tmp && \
     conda clean --all -f -y
 
 # Install PostgreSQL in a dedicated conda environment.
-RUN conda create -c conda-forge -n pgsql postgresql=10 && conda clean --all -f -y
+RUN conda create -c conda-forge -n pgsql postgresql=12 && conda clean --all -f -y
 
 # Below is a solution to a strange bug with PGSQL=10
 # Taken from https://github.com/tethysplatform/tethys/issues/667.
@@ -140,5 +140,8 @@ RUN sed -i 's/^#force_color_prompt=yes/force_color_prompt=yes/' /etc/skel/.bashr
 # Always activate conda.
 COPY profile.d/activate_conda.sh /etc/profile.d/
 
+# Add database migration script.
+COPY opt/migrate-database.sh /opt/migrate-database.sh
+
 # Use baseimage-docker's init system.
 CMD ["/sbin/my_init"]
diff --git a/opt/migrate-database.sh b/opt/migrate-database.sh
new file mode 100755
index 0000000..64c3dcd
--- /dev/null
+++ b/opt/migrate-database.sh
@@ -0,0 +1,59 @@
+#!/bin/bash
+set -exuo pipefail
+
+# This script is intended to be run in a container. Its job is to migrate the PGSQL database to a newer version.
+
+# The following variables are required:
+DB_FOLDER=/home/${SYSTEM_USER}/.postgresql
+
+OLD_PGSQL_DB_VERSION=`cat ${DB_FOLDER}/PG_VERSION`  # The version of the database before the upgrade is taken from the PG_VERSION file.
+NEW_PGSQL_DB_VERSION=`conda run -n pgsql psql -V | awk '{ print int( $3 ) }'`  # The new version of PGSQL is given by the `psql -V` command installed in the pgsql conda environment.
+
+TIMESTAMP=$(date +%Y%m%d%H%M%S)
+BACKUP_DB_FOLDER=/home/${SYSTEM_USER}/.postgresql-bak-${TIMESTAMP}
+OLD_DB_CONDA_ENV_NAME="pgsql-backup-${OLD_PGSQL_DB_VERSION}-${TIMESTAMP}"
+DUMP_FILE_NAME="/home/${SYSTEM_USER}/pgsql-dump-${OLD_PGSQL_DB_VERSION}-${TIMESTAMP}.sql"
+
+# Make sure the new PostgreSQL server is shut down.
+conda run -n pgsql pg_ctl -D ${DB_FOLDER} stop || true # Ignore errors, as the database might not be running.
+
+# Part 1: dump the old database.
+
+# Make a backup of the database.
+mv ${DB_FOLDER} ${BACKUP_DB_FOLDER}
+
+# Install the old version of PostgreSQL.
+conda create -c conda-forge --yes -n ${OLD_DB_CONDA_ENV_NAME} postgresql=${OLD_PGSQL_DB_VERSION} && conda clean --all -f -y
+
+# Below is a solution to a strange bug with PGSQL=10
+# Taken from https://github.com/tethysplatform/tethys/issues/667.
+# This bug is not present for PGSQL=14. So as soon as we migrate, the line below can be removed.
+if [ ${OLD_PGSQL_DB_VERSION} -eq 10 ]; then
+    cp /usr/share/zoneinfo /home/aiida/.conda/envs/${OLD_DB_CONDA_ENV_NAME}/share/ -R
+fi
+
+# Start the old version of PostgreSQL.
+conda run -n ${OLD_DB_CONDA_ENV_NAME} pg_ctl -D ${BACKUP_DB_FOLDER} -l ${BACKUP_DB_FOLDER}/logfile start
+
+# Dump the old database.
+conda run -n ${OLD_DB_CONDA_ENV_NAME} pg_dumpall -f ${DUMP_FILE_NAME}
+
+# Stop the old version of PostgreSQL.
+conda run -n ${OLD_DB_CONDA_ENV_NAME} pg_ctl -D ${BACKUP_DB_FOLDER} stop
+
+# Delete the environment with old version of PostgreSQL.
+conda env remove -n ${OLD_DB_CONDA_ENV_NAME}
+
+# Part 2: restore the old database to the new version.
+
+# Create a new database.
+conda run -n pgsql initdb -D ${DB_FOLDER}
+
+# Start the new version of PostgreSQL.
+conda run -n pgsql pg_ctl -w -D ${DB_FOLDER} -l ${DB_FOLDER}/logfile start
+
+# Restore the old database.
+conda run -n pgsql psql -f ${DUMP_FILE_NAME} postgres
+
+# Stop the new version of PostgreSQL to return everything to the original state.
+conda run -n pgsql pg_ctl -D ${DB_FOLDER} stop
diff --git a/opt/start-postgres.sh b/opt/start-postgres.sh
index 20ac98e..6bbff92 100755
--- a/opt/start-postgres.sh
+++ b/opt/start-postgres.sh
@@ -29,6 +29,11 @@ else
     if ! $running ; then
        echo "" > /home/${SYSTEM_USER}/.postgresql/logfile # empty log files
        rm -vf /home/${SYSTEM_USER}/.postgresql/postmaster.pid
-       ${PSQL_START_CMD}
+       ${PSQL_START_CMD} || cant_start=true
+   fi
+
+   if $cant_start; then
+      echo "Postgresql could not be started. Maybe the database needs to be migrated."
+      touch /home/$SYSTEM_USER/.PGSQL_MIGRATION_REQUIRED
    fi
 fi