Battle of Waterloo
Although they had not taken casualties, IV Corps had been marching for two days, covering the retreat of the three other corps of the Prussian army from the battlefield of Ligny. They had been posted farthest away from the battlefield, and progress was very slow.
The roads were in poor condition after the night's heavy rain, and Bülow's men had to pass through the congested streets of Wavre and move 88 artillery pieces. Matters were not helped when a fire broke out in Wavre, blocking several streets along Bülow's intended route. As a result, the last part of the corps left at 10:00, six hours after the leading elements had moved out towards Waterloo. Bülow's men were followed to Waterloo first by I Corps and then by II Corps.
Napoleon breakfasted off silver plate at Le Caillou, the house where he had spent the night. When Soult suggested that Grouchy should be recalled to join the main force, Napoleon said, "Just because you have all been beaten by Wellington, you think he's a good general. I tell you Wellington is a bad general, the English are bad troops, and this affair is nothing more than eating breakfast".
Napoleon's seemingly dismissive remark may have been strategic, given his maxim "in war, morale is everything". He had acted similarly in the past, and on the morning of the battle of Waterloo may have been responding to the pessimism and objections of his chief of staff and senior generals.

Later on, being told by his brother, Jerome, of some gossip overheard by a waiter between British officers at lunch at the King of Spain inn in Genappe that the Prussians were to march over from Wavre, Napoleon declared that the Prussians would need at least two days to recover and would be dealt with by Grouchy. Surprisingly, Jerome's overheard gossip aside, the French commanders present at the pre-battle conference at Le Caillou had no information about the alarming proximity of the Prussians and did not suspect that Blücher's men would start erupting onto the field of battle in great numbers just five hours later.
Napoleon had delayed the start of the battle owing to the sodden ground, which would have made manoeuvring cavalry and artillery difficult. In addition, many of his forces had bivouacked well to the south of La Belle Alliance. At 10:00, in response to a dispatch he had received from Grouchy six hours earlier, he sent a reply telling Grouchy to "head for Wavre [to Grouchy's north] in order to draw near to us [to the west of Grouchy]" and then "push before him" the Prussians to arrive at Waterloo "as soon as possible".
At 11:00, Napoleon drafted his general order: Reille's Corps on the left and d'Erlon's Corps to the right were to attack the village of Mont-Saint-Jean and keep abreast of one another. This order assumed Wellington's battle-line was in the village, rather than at the more forward position on the ridge. To enable this, Jerome's division would make an initial attack on Hougoumont, which Napoleon expected would draw in Wellington's reserves, since its loss would threaten his communications with the sea. A grande batterie of the reserve artillery of I, II, and VI Corps was to then bombard the centre of Wellington's position from about 13:00. D'Erlon's corps would then attack Wellington's left, break through, and roll up his line from east to west. In his memoirs, Napoleon wrote that his intention was to separate Wellington's army from the Prussians and drive it back towards the sea.

Hougoumont: Historian Andrew Roberts notes that "It is a curious fact about the Battle of Waterloo that no one is absolutely certain when it actually began". Wellington recorded in his dispatches that at "about ten o'clock [Napoleon] commenced a furious attack upon our post at Hougoumont". Other sources state that the attack began around 11:30. The house and its immediate environs were defended by four light companies of Guards, and the wood and park by Hanoverian Jäger and the 1/2nd Nassau.
The initial attack by Bauduin's brigade emptied the wood and park, but was driven back by heavy British artillery fire, and cost Bauduin his life. As the British guns were distracted by a duel with French artillery, a second attack by Soye's brigade and what had been Bauduin's succeeded in reaching the north gate of the house. Sous-Lieutenant Legros, a French officer, broke the gate open with an axe, and some French troops managed to enter the courtyard. The Coldstream Guards and the Scots Guards arrived to support the defence. There was a fierce melee, and the British managed to close the gate on the French troops streaming in. The Frenchmen trapped in the courtyard were all killed.
Fighting continued around Hougoumont all afternoon. Its surroundings were heavily invested by French light infantry, and coordinated attacks were made against the troops behind Hougoumont. Wellington's army defended the house and the hollow way running north from it. In the afternoon, Napoleon personally ordered the house to be shelled to set it on fire, resulting in the destruction of all but the chapel. Du Plat's brigade of the King's German Legion was brought forward to defend the hollow way, which they had to do without senior officers. Eventually they were relieved by the 71st Highlanders, a British infantry regiment. Adam's brigade was further reinforced by Hugh Halkett's 3rd Hanoverian Brigade, and successfully repulsed further infantry and cavalry attacks sent by Reille. Hougoumont held out until the end of the battle.

I had occupied that post with a detachment from General Byng's brigade of Guards, which was in position in its rear; and it was some time under the command of Lieutenant-Colonel MacDonald, and afterwards of Colonel Home; and I am happy to add that it was maintained, throughout the day, with the utmost gallantry by these brave troops, notwithstanding the repeated efforts of large bodies of the enemy to obtain possession of it.
When I reached Lloyd's abandoned guns, I stood near them for about a minute to contemplate the scene: it was grand beyond description. Hougoumont and its wood sent up a broad flame through the dark masses of smoke that overhung the field; beneath this cloud the French were indistinctly visible. Here a waving mass of long red feathers could be seen; there, gleams as from a sheet of steel showed that the cuirassiers were moving; 400 cannon were belching forth fire and death on every side; the roaring and shouting were indistinguishably commixed—together they gave me an idea of a labouring volcano. Bodies of infantry and cavalry were pouring down on us, and it was time to leave contemplation, so I moved towards our columns, which were standing up in square.
The fighting at Hougoumont has often been characterised as a diversionary attack to draw in Wellington's reserves which escalated into an all-day battle and drew in French reserves instead. In fact there is a good case to believe that both Napoleon and Wellington thought that holding Hougoumont was key to winning the battle. Hougoumont was a part of the battlefield that Napoleon could see clearly, and he continued to direct resources towards it and its surroundings all afternoon (33 battalions in all, 14,000 troops). Similarly, though the house never contained a large number of troops, Wellington devoted 21 battalions (12,000 troops) over the course of the afternoon in keeping the hollow way open to allow fresh troops and ammunition to reach the buildings. He moved several artillery batteries from his hard-pressed centre to support Hougoumont, and later stated that "the success of the battle turned upon closing the gates at Hougoumont". Much like the fight for Little Round Top during the Battle of Gettysburg in the US Civil War some fifty years later, the struggle for Hougoumont became the key battle within the battle. Hougoumont proved to be decisive terrain.

The Grand Battery starts its bombardment: The 80 guns of Napoleon's grande batterie drew up in the centre. These opened fire at 11:50, according to Lord Hill (commander of the Anglo-allied II Corps), while other sources put the time between noon and 13:30. The grande batterie was too far back to aim accurately, and the only other troops they could see were skirmishers of the regiments of Kempt and Pack, and Perponcher's 2nd Dutch division (the others were employing Wellington's characteristic "reverse slope defence").
The bombardment caused a large number of casualties. Although some projectiles buried themselves in the soft soil, most found their marks on the reverse slope of the ridge. The bombardment forced the cavalry of the Union Brigade (in third line) to move to its left, to reduce their casualty rate.

Napoleon spots the Prussians: At about 13:15, Napoleon saw the first columns of Prussians around the village of Lasne-Chapelle-Saint-Lambert, 4 to 5 miles (6.4 to 8.0 km) away from his right flank—about three hours march for an army.