Hyperborean: Spies. Save up and use espionage to buy spies in the enemy countries, and then you can use the espionage options to spy on cities. When you do that, you see a lot of useful information, and if you look at how their economy is being used at the bottom of the espionage report screen you will see the distribution of science/shields/cash. Thats where I found out what they were spending on research.
I have to check it out. I only use spies to find out how many units the AI has. I don't want to risk losing my spy by conducting any operations. I hate it when I can't see the forces of my opponents (and allies). But maybe I should try it on some minor nation in South America to see for myself.
But after you have played for a while you'll learn who is ahead of you on research, and who's behind anyway. I know that the British AI is ahead of me, and that the Soviets are far, far behind.
Germany - Sid - Week 25, 1941
Cities conquered: Tver, Moscow, Tula, Voronezh, Kursk, Groznyj, Timbuktu and Corsica (again).
Things are finally starting to go my way.

I think the key to the success was to heavily reinforce the Luftwaffe. I can obliterate dozens of divisions every week now, and that has really helped the Wehrmacht. There are still some pockets of resistance behind the front lines, but they can easily be wiped out.
Because of the Allied domination in the Mediterranean I have not been able to reinforce DAK as I had planned. But I still have enough panzers to move forward. I have airdropped all my paratroopers over North Africa, and they are holding the conquered cities until I can develop the paratrooper plane and reinforce the garrisons by air. I have almost finished researching Air 2 1940, so this shouldn't take too long.
I have 2 u-boats in the Red Sea (where they have engaged and sunk several destroyers), 2 u-boats near India, 2 u-boats around Australia, 2 u-boats west of South America, 1 u-boat north of Japan (this one took the Northwest Passage to the Pacific Ocean, and it has sunk several Soviet subs). I also had a u-boat in Indonesia, but the British sunk it. And a few more subs are currently in the Northwest passage on their way to the Pacific.
Japan has conquered Lucknow. Guam is Japanese. Truk is British. New Soviet capital: Sverdlovsk.
Now that I have connected all Spanish cities with railroads (except La Coruna, where the Allies prevent me from building anything) I have noticed what an effort it takes to build railroads, and this is good. For instance, I have 102 workers building a railroad on a mountain tile, and they are still not done!
The RAF bombings have almost stopped now that Luftwaffe has been reinforced. With over 100 fighters they don't dare to attack me as often as they once did. My only trouble comes when I take a new city within RAFs reach. They will bomb it with everything they have.
My fleet of Bismarcks has been entangled in battles in the English Channel. They are pretty good. I destroy two KGVs for every Bismarck they sink. But I'm not entirely happy with the kill ratio. I want to cause more damage.
I'm going to reward my Finnish allies by starting to hand over the cities I have taken in northwestern Russia to them. This is for two reasons. First of all, I want a strong ally, and secondly, I want them to have access to the Atlantic. That's why I'm going to give them the city-ports of Narvik, Murmansk, Sosnovka, Arkhangelsk and Petjora (I'm going to keep southern Scandinavia though. The border will be drawn south of Narvik-Kiruna-Luleå.).
I may consider giving the Italians some African cities, but that is a later issue. Right now I have to focus on winning the Eastern front.
Now that I have pushed the Russians back I'm going to reform the Army Groups. Army Group North's objectives are Gorki, Kazan and Perm. Army Group Centre's objectives are Saratov and Kujbysjev. Army Group South's objectives are Stalingrad and Astrachan. My artillery will move to Stalingrad to attack the fortress there while my panzers will carry out the other operations.
Once these objectives have been completed I'm going to reform the Army Groups again. I will replace Army Group Centre's panzers with infantry, supported by artillery, after Stalingrad has been taken. The reason is because the panzers cannot use their speed when they move through forests. Instead Army Group South will be reinforced by the panzers and attack Central Asia, and link up with the Japanese. Army Group North will consist entirely of panzers, and they will attack the northernmost Siberian cities where I have most use of their speed on the tundra. This involves some pretty complex moves back and forth along the battle-lines, but I think it will work.
I know I said earlier that I would attack Suez with Army Group South, but those plans have been postponed for a while, mainly because I still don't have control over the Mediterranean, and it will take some time before I will. So there's no rush. I think it's more important to make contact with the Japanese and threaten the British and the Russians from Central Asia. That's my number one priority right now.
List of units week 25, 1941
(Changes from week 1, 1941 in parenthesis)
Workers: 123 (78)
Transports: 4 (-6)
Special transport: 1
Destroyers: 3 (-8)
Heavy cruisers: 0 (-2)
Bismarcks: 9 (9)
Coastal submarines: 11
Type VIII: 8 (-2)
Type IX: 24 (-8)
German Army HQ: 5
Heavy artillery: 26
Flak: 13
German 88: 37 (14)
Panzer II: 1 (-1)
Panzer IIIe: 95 (19)
Marines: 1 (-2)
Paratroopers: 4 (1)
German Security Divisions: 3 (-2)
German infantry: 97 (33)
Slovakia infantry: 7 (2)
Hungary infantry: 13 (1)
Romania infantry: 30 (5)
Bulgaria infantry: 14 (3)
Do-17: 3 (-1)
Ju87B: 14 (6)
Ju 88: 28 (17)
Heinkel-111: 4 (1)
ME-109: 99 (55)
ME-110: 14 (11)
. . . . . . . . . Germany Soviet . . . . U.K. . . . U.S. . . . . Japan . . France . Italy . . Finland
Workers: . . . 123 (78) 70 (-29) . . 122 (6) . 70 (1) . . . 51 . . . . 13 (-5) . 9 (3) . . 10
Infantry: . . . 164 (42) 306 (-190) 490 (-6) . 579 (218) 333 (50) 48 (-28) . 68 (6) . 60 (11)
Tanks: . . . . 96 (18) . 75 (-10) . . 184 (72) . 97 (80) . 51 (-31) . -- . . . . -- . . . . 15 (7)
Artillery: . . . 31 . . . . 57 (-7) . . . 19 (4) . . 26 . . . . . 30 (19) . . 7 (4) . . -- . . . . 5
Planes: . . . . 162 (89) 115 (32) . . 122 . . . . 97 (22) . 93 (17) . . 4 (-3) . 6 (-6) . 1
Transports: . 5 (-6) . . 1 (-1) . . . . 23 (-2) . 3 (1) . . . 16 (2) . . . -- . . . -- . . . . 1
Submarines: . 43 (-10) 3 (-6) . . . . 4 (-3) . . 12 (-10) . 1 (1) . . . -- . . . -- . . . . --
Destroyers: . 3 (-8) . . 0 (-2) . . . . 40 (3) . . 1 (-5) . . 27 (1) . . . -- . . . -- . . . . --
Cruisers: . . . 0 (-2) . . 0 . . . . . . . 12 . . . . . 1 . . . . . 2 . . . . . . -- . . . -- . . . . --
Capital ships: 9 (4) . . . 0 . . . . . . . 41 (1) . . 22 (6) . . 48 (4) . . -- . . . -- . . . . --
Carriers: . . . . -- . . . . -- . . . . . . . -- . . . . 1 (-1) . . 6 . . . . . . -- . . . -- . . . . --
Flak: . . . . . . 13 . . . . 2 (2) . . . . . 7 (-1) . 13 (10) . . -- . . . . . -- . . . -- . . . . --
Paratroopers: 4 (1) . . 0 . . . . . . . . 3 (1) . . 5 (3) . . . 1 . . . . . . -- . . . 1 (1) . . . --
Marines: . . . . 1 (-2) . 0 . . . . . . . 1 . . . . . 130 (68) . 1 . . . . . . -- . . . -- . . . . --
Cavalry: . . . . -- . . . . 3 (-1) . . . . 8 (3) . . 14 (7) . . . -- . . . . . 27 (3) -- . . . . --
Motorized inf: -- . . . . 68 (-43) . . . -- . . . . -- . . . . . -- . . . . . -- . . . -- . . . . --