The Italian Trenitalia train service connects Monaco to Italian cities like Milan, Genoa, Rome and Venice. Connections are generally made in Ventimiglia, the first train station in Italy after the French-Italian border.
You can consult TGV-Europe for all European train travel. The major Europeans cities are well linked via the European rail network.
If you are coming from the UK, Eurostar is the high-speed passenger train from London to Paris & London to Brussels, which travels via the Channel Tunnel. Not to be confused with Eurotunnel, the company which owns the Channel Tunnel whose car-carrying trains shuttle road vehicles across the Channel. Eurostar carries passengers, not cars. They now run a direct train from London to Lyon, Avignon & Marseille between one and five times a week all year round.
Eurotunnel provides a quick and simple method to get you and your car from England to France. From Folkestone to Calais in only 35 minutes, it is the fastest way to get across (or under) the English Channel. There are around four departures every hour - and as always you should book early to get the best rates.
Russian Railways now run a weekly year round service from Moscow to Nice, stopping in Monaco. You leave Moscow on a Thursday and arrive in Nice on Saturday morning. The train also stops at Minsk, Warsaw, Vienna and Verona, amongst others. Travel time is around 47 hours. Moscow-Nice is one of the longest trans-European routes at a distance of 3315 km. Originally the route was popular with Russian aristocracy of 19th-century. It has existed since 1864 when first trains started running from Russia to Nice.