What was the extent of Soviet war crimes in the Second World War?

The Soviet Union unquestionably committed widespread war crimes, both during their westward expansion in 1939 and 1940 and as they overran the Axis forces in 1944 and 1945. These included both famous events, such as the Katyn massacre and the deportation of the Crimean Tatars, and less famous ones, such as mistreatment of Axis prisoners of war.

The first Soviet war crimes occurred during the invasion of Poland in 1939. The NKVD followed the Red Army into Poland and quickly began arresting people who were perceived as opponents of the Soviet regime, including military and political leaders as well as intellectuals; this closely mirrors the Intelligenzaktion carried out by the Nazis during the German occupation of Poland. The Soviets deported hundreds of thousands of Poles, in addition to over 300,000 prisoners of war (of whom about 100,000 died in captivity). Many of the deportees died during the deportation, and a large number of those arrested by the NKVD were later killed or died during torture. (Tadeusz Piotrowski, Poland's Holocaust; Jan T. Gross, Revolution from Abroad) The most notable example of killings by the NKVD is the Katyn Massacre, in which over 20,000 Polish officers and intellectuals were murdered in a forest near Katyn, RSFSR. The Germans discovered the graves of the Katyn victims in 1943, and while there were attempts by the Soviets to frame this as German propaganda, we now know the massacres were carried out by the NKVD. (Thomas Urban, The Katyn Massacre 1940)

The Soviets carried out similar actions during the occupation of the Baltic States, as well as the Romanian territories of Bessarabia and Bukovina, in 1940-1941. About 10,000 Estonians, 20,000 Lithuanians, and 35,000 Latvians were deported by the Soviets, and similar purges of the political and intellectual leadership were carried out by the NKVD. (See the reports of the Estonian and Lithuanian commissions on the Soviet and Nazi occupations) In Bessarabia and Bucovina, there were several massacres of civilians, in addition to deportations of ethnic Romanians, after the Soviets seized Bessarabia and northern Bukovina from Romania on 28 June 1940; a famous case was the Fântâna Albă massacre in Bukovina on 1 April 1941, where the Soviet border guards shot an uncertain number of ethnic Romanians trying to cross the border into Romania. (Aurelian Lavric, "Politica de represiune a regimului sovietic în sudul Basarabiei și nordul Bucovinei: 1940–1941, 1944–1945")

The NKVD also massacred prisoners as the Soviets were retreating eastward in 1941 during Operation Barbarossa. There were several reports of the Axis forces arriving and discovering the bodies of prisoners who had been shot by the NKVD just before they arrived. Of course, we can't just accept these Axis reports uncritically, but testimony from local civilians supports their claims. (Bogdan Musial, Konterrevolutionäre Elemente sind zu erschießen. Die Brutalisierung des deutsch-sowjetischen Krieges im Sommer 1941)

As the Soviets advanced westward from 1943 to 1945, there were several deportations of ethnic minorities, including Kalmyks, Tatars, Ingushetians, and Chechens. These groups were collectively accused of collaboration with the Nazis, which was used as justification for ethnic cleansing. While there certainly were members of these groups who collaborated with the Nazis (just as there were Russians, Ukrainians, etc. who collaborated), it's clear that this was simply a pretext for Stalin's ethnic cleansing policy. These actions have been condemned by various authorities as crimes against humanity, and, in the case of the Chechens, genocide. (Pavel Polian, Against Their Will)

The Soviets also systematically mistreated Axis prisoners of war, including massacres of groups of prisoners (e.g. at Feodosia, in Crimea, in 1942). Axis POWs were subjected to long forced marches to POW camps, where they faced conditions that included inadequate food and medical care. According to Soviet records, about 20% of the 2.5 million German POWs taken by the Soviets died in captivity. However, the actual number could be much higher, perhaps on the order of 1 million. (Rüdiger Overmans, Deutsche Militärverluste im Zweiten Weltkrieg)

Finally, there were war crimes that were carried out during the Soviet offensives and occupation in Eastern Europe. These included looting of food and other property from civilians, widespread rape, and killing of civilians. Such actions are documented in Poland, Hungary, Romania, Yugoslavia, Czechoslovakia, and Germany. The Soviets also carried out arrests and deportations of civilian populations, particularly ethnic Germans, in Poland, Hungary, Romania, and Czechoslovakia. The NKVD carried out another series of arrests and repressions during the occupation of Eastern Europe. Among the notable victims was Raoul Wallenberg, a Swedish diplomat who saved thousands of Hungarian Jews from deportation to Auschwitz by giving them Swedish passports; he later died in Soviet captivity, and was named Righteous Among the Nations by Yad Vashem. (Antony Beevor, Berlin: The Downfall, 1945; Alfred Maurice de Zayas, A Terrible Revenge; Adrian Cioroianu, Pe umerii lui Marx. O introducere în istoria comunismului românesc)

There's a lot I couldn't cover in the space of a reddit post, but suffice to say that Soviet war crimes were very extensive, with millions of victims across a broad area of Eastern and Central Europe. Unfortunately, as with many things where the Soviet Union is involved, political biases often distort the historical and public understanding in the West, but hopefully I've given you a starting point on some sources which document these crimes. If you're looking for a "one-stop shop", I'd recommend Norman Davies' Europe at War 1939-1945: No Simple Victory. There's also Timothy Snyder's Bloodlands: Europe between Hitler and Stalin, which is...sort of problematic from a conceptual perspective, but a generally accurate history nonetheless.