After officially arriving in India on June 5, the southwest monsoon has been slow to progress across the rest of the country. It made its way to India's north east region quite rapidly, along with parts of south Tamil Nadu, and coastal Karnataka, Goa and Maharastra. However, it stagnated in Maharastra for nearly a week.
The weather bureau finally confirmed that the monsoon had hit in Mumbai yesterday, despite the city receiving widespread heavy rain the previous weekend. Apparently, the monsoon is only declared when the wind starts coming from a southwesterly direction.
According to this news report, which gives the forecast for this week, the monsoon also arrived in Orissa yesterday and Delhi got some refreshing, much needed, pre-monsoon showers today. The monsoon has now advanced into more of Madhya Pradesh, Maharashtra, the interior of Karnataka (including Bangalore), most of Tamil Nadu, the remainder of the south Bay of Bengal, and more of the central and north Bay of Bengal.
Rainfall has been disappointingly lower than normal though, with this news report saying that Scotland (in the UK) is wetter than India's monsoon season, with almost four inches of rain received there over the weekend!
More About the Monsoon in India:

Monsoon at Marine Drive, Mumbai