I'm not sure what level of complexity you're looking for, but there are some pretty complex combos that have been viable over the years, even in formats that don't use some of the older "broken" cards. One popular strategy for a while in the "Modern" format, which doesn't allow cards for the first 10 years or so of the game, used a mechanic called "Storm" where a spell would be copied for every spell you previously cast in the same turn. A card called Grapeshot had this ability and did 1 damage, so the deck played creatures that made your spells cost less mana and spells that gave you extra mana or draw cards, and the goal was to cast 19 spells and then grapeshot your opponent for their entire starting life total of 20, often as early as on their fourth turn. It was consistent enough that it was a staple in the format for at least a few years (although I haven't kept up with the meta as much for a few years now). Another higher variance but potentially even faster combo used a creature called Griselbrand, which let you pay 7 life to draw 7 cards, a bunch of mana "rituals" like storm, and used a card called Nourishing Shoal to let you exile certain cards from your hand to gain life. The win condition was typically to draw at least 7 lands and cast a creature that let you discard a land to do 3 damage, and it could potentially do this on the very first turn, although eventually one of the cards that was necessary for it to function got banned in modern, although by then Griselbrand decks weren't really ever played due to there being far more consistent options with better ability to deal with an opponent trying to thwart their game plan. If you include Legacy (which allows cards from any point in the history of the game but still with a custom ban list) or Vintage (where all cards are allowed but some are "restricted" to only one copy instead of the typical 4 per deck), there are even more powerful combos you can take advantage of.

Combo decks have always and likely will always be a part of the meta for most formats, although to varying degrees depending on how many cards the format has available and how effective it happens to be in the current meta. It's considered one of the three main deck archetypes along with "control" decks that attempt to shut down what the opponent is trying to do and slowly build an advantage over time and "aggro" which use a more straightforward approach of just attacking the opponent with creatures or spells (or both). Not everything cleanly fits into one of those strategies of course, and even a deck that has a win condition that fits into one archetype might dip into the other as a backup plan (e.g. a combo deck with control elements that help it buy time if it can't get off the combo as quickly as it would prefer, or a control deck with some efficient creatures that it can use for a surprise attack if the circumstance makes sense), but even in a setting like playing a few games at a card shop on a Friday night, seeing a combo deck with the level of complexity described above isn't really uncommon at all.

That said, I've read that a lot of the hardest cards to program tend to be the ones that subvert the basic expectations of the game. One infamous example that comes to mind is a creature that after being cast added an extra turn after yours where you controlled your opponent, after which they took their regular turn and the turn order resumed its previous alternation. Programming that would require adding in the ability to show one player's hidden game state to the other, let them make any sort of decisions using their cards that the player would normally do (short of literally conceding the game) and inserting an extra turn in the order with that weird control mechanism...all just for one card out of tens of thousands! Obviously most cards are not that complex, and Arena specifically doesn't attempt to support literally every card in existence and instead supports cards going back to its initial stable release along with explicitly chosen cards added to special Arena-only sets in order to introduce them, but when its an explicit rule that the text on the card overrides the normal rules of the game when they disagree, it very quickly gets to the point where you need to consider that there will likely be an edge cast for almost any possible state transition.