The wall leaks after rain - how do I seal it from the outside?

First, look at what level the water appears at and how it spreads across the wall. If only one spot gets wet after a heavy rain, there's likely a localized problem - a crack, an unclosed seam, or a gap around the downspout. But if moisture shows up across the whole surface or appears on the inside of the wall far from any visible damage, sealant will only buy you time.

I agree with the previous answer that you need to figure out the cause, but you can still grab some sealant right away - it won't hurt. Check the seams between bricks or panels, the joints around windows and doors, the cornices, the gutters. Clean out the gaps from dirt and moss, let them dry for at least a couple of days after rain. For exterior sealing, polyurethane sealant works well (it holds up and isn't bothered by frost) or silicone - apply it into deep gaps and along the mortar joints.

But if that doesn't fix it, it's more serious: the internal waterproofing might be compromised, there could be missing vapor barrier, or voids might have formed in the masonry. Then you need to call a specialist who can check with a moisture meter to see exactly where water is pooling inside the wall. Sometimes the problem is solved by redoing the foundation apron around the house or clearing out the gutters - the water's running off in the wrong direction.

Water usually comes in from a place that's not where you see it. That's the main problem with leaks - it can seep in a meter higher up the wall, work its way inside, and run down, then show up somewhere completely different. So just sealing the spot where you see moisture often doesn't help.

When you're looking for where it's coming from, check the eaves, gutters, and the roof over that section. Most of the time water gets in from outside there, not straight through the wall. If the gutter's clogged with leaves or there's a crack in the roof - that's easier to fix than redoing the whole facade waterproofing. Also check how the mortar joints are doing right above the leak spot; they usually break down first and become the main path for water.

Once you've figured out where the water's getting in, then you seal it up. Cracks and gaps in the masonry are better off widened a bit and filled with special sealant or facade-grade cement mortar - just smearing regular compound on the surface doesn't work very well. If the wall itself is intact but soaking up water over a large area, you need hydrophobic sealant or facade paint with water-repellent properties. The key thing is to fix what's letting water in there in the first place, not just plug the holes.

After rain, check the gutters too - they're often clogged with leaves or damaged, and water just pours past them straight onto the wall. If the gutters are fine, then yeah, look at the cracks and seams - caulk or cement mortar should be doing the job.