The home timeline is Twitter's hardest problem:
Pull model: Query followers' tweets on request. Simple but slow for users following many accounts.
Push model (fanout): When user tweets, write to all followers' timelines. Fast reads but expensive writes. Celebrity with M followers means M writes.
Hybrid: Push for normal users, pull for celebrities. Most users see pre-computed timelines. Celebrity tweets merged at read time.
Storage: Redis sorted sets for timelines. Score by timestamp. Trim old tweets to bound size.
Trade-off: Push optimizes reads. Pull optimizes writes. Choose based on read/write ratio.